n=5, k0=2, k1=0
Optimal Minimum Distance: 3
Generator Matrices that generate Codes having Optimal Minimum Distance: 30, 31, 32, 44, 47, 48, 52, 54, 56, 60, 62, 63,
Total No. of Codes having Optimal Minimum Distance: 12
Generator Matrices that generate Nice Codes : 1,
Total No. of Nice Codes: 1
Generator Matrix-1
a 0 0 0 0
0 a 0 0 0
b 0 0 0 0
0 b 0 0 0
Codewords:
0 0 0 0 0
0 b 0 0 0
b 0 0 0 0
b b 0 0 0
0 a 0 0 0
0 c 0 0 0
b a 0 0 0
b c 0 0 0
a 0 0 0 0
a b 0 0 0
c 0 0 0 0
c b 0 0 0
a a 0 0 0
a c 0 0 0
c a 0 0 0
c c 0 0 0
dmin: 1
Weight Enumerator: 1x0 + 6x1 + 9x2 + 0x3 + 0x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)4 (X_b)1 + (X_0)4 (X_b)1 + (X_0)3 (X_b)2 + (X_0)4 (X_a)1 + (X_0)4 (X_c)1 + (X_0)3 (X_a)1 (X_b)1 + (X_0)3 (X_b)1 (X_c)1 + (X_0)4 (X_a)1 + (X_0)3 (X_a)1 (X_b)1 + (X_0)4 (X_c)1 + (X_0)3 (X_b)1 (X_c)1 + (X_0)3 (X_a)2 + (X_0)3 (X_a)1 (X_c)1 + (X_0)3 (X_a)1 (X_c)1 + (X_0)3 (X_c)2
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
0 0 0 a 0
0 0 0 a a
0 0 0 a b
0 0 0 a c
0 0 0 b 0
0 0 0 b a
0 0 0 b b
0 0 0 b c
0 0 0 c 0
0 0 0 c a
0 0 0 c b
0 0 0 c c
0 0 a 0 0
0 0 a 0 a
0 0 a 0 b
0 0 a 0 c
0 0 a a 0
0 0 a a a
0 0 a a b
0 0 a a c
0 0 a b 0
0 0 a b a
0 0 a b b
0 0 a b c
0 0 a c 0
0 0 a c a
0 0 a c b
0 0 a c c
0 0 b 0 0
0 0 b 0 a
0 0 b 0 b
0 0 b 0 c
0 0 b a 0
0 0 b a a
0 0 b a b
0 0 b a c
0 0 b b 0
0 0 b b a
0 0 b b b
0 0 b b c
0 0 b c 0
0 0 b c a
0 0 b c b
0 0 b c c
0 0 c 0 0
0 0 c 0 a
0 0 c 0 b
0 0 c 0 c
0 0 c a 0
0 0 c a a
0 0 c a b
0 0 c a c
0 0 c b 0
0 0 c b a
0 0 c b b
0 0 c b c
0 0 c c 0
0 0 c c a
0 0 c c b
0 0 c c c
Is it a nice code?: Yes
Generator Matrix-2
a 0 0 0 0
0 a 0 0 a
b 0 0 0 0
0 b 0 0 b
Codewords:
0 0 0 0 0
0 b 0 0 b
b 0 0 0 0
b b 0 0 b
0 a 0 0 a
0 c 0 0 c
b a 0 0 a
b c 0 0 c
a 0 0 0 0
a b 0 0 b
c 0 0 0 0
c b 0 0 b
a a 0 0 a
a c 0 0 c
c a 0 0 a
c c 0 0 c
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 3x2 + 9x3 + 0x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)4 (X_b)1 + (X_0)2 (X_b)3 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)2 (X_a)2 (X_b)1 + (X_0)2 (X_b)1 (X_c)2 + (X_0)4 (X_a)1 + (X_0)2 (X_a)1 (X_b)2 + (X_0)4 (X_c)1 + (X_0)2 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)2 (X_a)1 (X_c)2 + (X_0)2 (X_a)2 (X_c)1 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 0 a 0
0 0 0 b 0
0 0 0 c 0
0 0 a 0 0
0 0 a a 0
0 0 a b 0
0 0 a c 0
0 0 b 0 0
0 0 b a 0
0 0 b b 0
0 0 b c 0
0 0 c 0 0
0 0 c a 0
0 0 c b 0
0 0 c c 0
Is it a nice code?: No
Generator Matrix-3
a 0 0 0 0
0 a 0 a 0
b 0 0 0 0
0 b 0 b 0
Codewords:
0 0 0 0 0
0 b 0 b 0
b 0 0 0 0
b b 0 b 0
0 a 0 a 0
0 c 0 c 0
b a 0 a 0
b c 0 c 0
a 0 0 0 0
a b 0 b 0
c 0 0 0 0
c b 0 b 0
a a 0 a 0
a c 0 c 0
c a 0 a 0
c c 0 c 0
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 3x2 + 9x3 + 0x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)4 (X_b)1 + (X_0)2 (X_b)3 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)2 (X_a)2 (X_b)1 + (X_0)2 (X_b)1 (X_c)2 + (X_0)4 (X_a)1 + (X_0)2 (X_a)1 (X_b)2 + (X_0)4 (X_c)1 + (X_0)2 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)2 (X_a)1 (X_c)2 + (X_0)2 (X_a)2 (X_c)1 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
0 0 a 0 0
0 0 a 0 a
0 0 a 0 b
0 0 a 0 c
0 0 b 0 0
0 0 b 0 a
0 0 b 0 b
0 0 b 0 c
0 0 c 0 0
0 0 c 0 a
0 0 c 0 b
0 0 c 0 c
Is it a nice code?: No
Generator Matrix-4
a 0 0 0 0
0 a 0 a a
b 0 0 0 0
0 b 0 b b
Codewords:
0 0 0 0 0
0 b 0 b b
b 0 0 0 0
b b 0 b b
0 a 0 a a
0 c 0 c c
b a 0 a a
b c 0 c c
a 0 0 0 0
a b 0 b b
c 0 0 0 0
c b 0 b b
a a 0 a a
a c 0 c c
c a 0 a a
c c 0 c c
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 0x2 + 3x3 + 9x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)4 (X_b)1 + (X_0)1 (X_b)4 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_0)1 (X_a)3 (X_b)1 + (X_0)1 (X_b)1 (X_c)3 + (X_0)4 (X_a)1 + (X_0)1 (X_a)1 (X_b)3 + (X_0)4 (X_c)1 + (X_0)1 (X_b)3 (X_c)1 + (X_0)1 (X_a)4 + (X_0)1 (X_a)1 (X_c)3 + (X_0)1 (X_a)3 (X_c)1 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
0 0 a 0 0
0 0 b 0 0
0 0 c 0 0
Is it a nice code?: No
Generator Matrix-5
a 0 0 0 0
0 a a 0 0
b 0 0 0 0
0 b b 0 0
Codewords:
0 0 0 0 0
0 b b 0 0
b 0 0 0 0
b b b 0 0
0 a a 0 0
0 c c 0 0
b a a 0 0
b c c 0 0
a 0 0 0 0
a b b 0 0
c 0 0 0 0
c b b 0 0
a a a 0 0
a c c 0 0
c a a 0 0
c c c 0 0
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 3x2 + 9x3 + 0x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)4 (X_b)1 + (X_0)2 (X_b)3 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)2 (X_a)2 (X_b)1 + (X_0)2 (X_b)1 (X_c)2 + (X_0)4 (X_a)1 + (X_0)2 (X_a)1 (X_b)2 + (X_0)4 (X_c)1 + (X_0)2 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)2 (X_a)1 (X_c)2 + (X_0)2 (X_a)2 (X_c)1 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
0 0 0 a 0
0 0 0 a a
0 0 0 a b
0 0 0 a c
0 0 0 b 0
0 0 0 b a
0 0 0 b b
0 0 0 b c
0 0 0 c 0
0 0 0 c a
0 0 0 c b
0 0 0 c c
Is it a nice code?: No
Generator Matrix-6
a 0 0 0 0
0 a a 0 a
b 0 0 0 0
0 b b 0 b
Codewords:
0 0 0 0 0
0 b b 0 b
b 0 0 0 0
b b b 0 b
0 a a 0 a
0 c c 0 c
b a a 0 a
b c c 0 c
a 0 0 0 0
a b b 0 b
c 0 0 0 0
c b b 0 b
a a a 0 a
a c c 0 c
c a a 0 a
c c c 0 c
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 0x2 + 3x3 + 9x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)4 (X_b)1 + (X_0)1 (X_b)4 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_0)1 (X_a)3 (X_b)1 + (X_0)1 (X_b)1 (X_c)3 + (X_0)4 (X_a)1 + (X_0)1 (X_a)1 (X_b)3 + (X_0)4 (X_c)1 + (X_0)1 (X_b)3 (X_c)1 + (X_0)1 (X_a)4 + (X_0)1 (X_a)1 (X_c)3 + (X_0)1 (X_a)3 (X_c)1 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
0 0 0 a 0
0 0 0 b 0
0 0 0 c 0
Is it a nice code?: No
Generator Matrix-7
a 0 0 0 0
0 a a a 0
b 0 0 0 0
0 b b b 0
Codewords:
0 0 0 0 0
0 b b b 0
b 0 0 0 0
b b b b 0
0 a a a 0
0 c c c 0
b a a a 0
b c c c 0
a 0 0 0 0
a b b b 0
c 0 0 0 0
c b b b 0
a a a a 0
a c c c 0
c a a a 0
c c c c 0
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 0x2 + 3x3 + 9x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)4 (X_b)1 + (X_0)1 (X_b)4 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_0)1 (X_a)3 (X_b)1 + (X_0)1 (X_b)1 (X_c)3 + (X_0)4 (X_a)1 + (X_0)1 (X_a)1 (X_b)3 + (X_0)4 (X_c)1 + (X_0)1 (X_b)3 (X_c)1 + (X_0)1 (X_a)4 + (X_0)1 (X_a)1 (X_c)3 + (X_0)1 (X_a)3 (X_c)1 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
Is it a nice code?: No
Generator Matrix-8
a 0 0 0 0
0 a a a a
b 0 0 0 0
0 b b b b
Codewords:
0 0 0 0 0
0 b b b b
b 0 0 0 0
b b b b b
0 a a a a
0 c c c c
b a a a a
b c c c c
a 0 0 0 0
a b b b b
c 0 0 0 0
c b b b b
a a a a a
a c c c c
c a a a a
c c c c c
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 0x2 + 0x3 + 3x4 + 9x5
Complete Weight Enumerator: (X_0)5 + (X_0)1 (X_b)4 + (X_0)4 (X_b)1 + (X_b)5 + (X_0)1 (X_a)4 + (X_0)1 (X_c)4 + (X_a)4 (X_b)1 + (X_b)1 (X_c)4 + (X_0)4 (X_a)1 + (X_a)1 (X_b)4 + (X_0)4 (X_c)1 + (X_b)4 (X_c)1 + (X_a)5 + (X_a)1 (X_c)4 + (X_a)4 (X_c)1 + (X_c)5
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-9
a 0 0 0 a
0 a 0 0 0
b 0 0 0 b
0 b 0 0 0
Codewords:
0 0 0 0 0
0 b 0 0 0
b 0 0 0 b
b b 0 0 b
0 a 0 0 0
0 c 0 0 0
b a 0 0 b
b c 0 0 b
a 0 0 0 a
a b 0 0 a
c 0 0 0 c
c b 0 0 c
a a 0 0 a
a c 0 0 a
c a 0 0 c
c c 0 0 c
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 3x2 + 9x3 + 0x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)4 (X_b)1 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)4 (X_a)1 + (X_0)4 (X_c)1 + (X_0)2 (X_a)1 (X_b)2 + (X_0)2 (X_b)2 (X_c)1 + (X_0)3 (X_a)2 + (X_0)2 (X_a)2 (X_b)1 + (X_0)3 (X_c)2 + (X_0)2 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_0)2 (X_a)2 (X_c)1 + (X_0)2 (X_a)1 (X_c)2 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 0 a 0
0 0 0 b 0
0 0 0 c 0
0 0 a 0 0
0 0 a a 0
0 0 a b 0
0 0 a c 0
0 0 b 0 0
0 0 b a 0
0 0 b b 0
0 0 b c 0
0 0 c 0 0
0 0 c a 0
0 0 c b 0
0 0 c c 0
Is it a nice code?: No
Generator Matrix-10
a 0 0 0 a
0 a 0 0 a
b 0 0 0 b
0 b 0 0 b
Codewords:
0 0 0 0 0
0 b 0 0 b
b 0 0 0 b
b b 0 0 0
0 a 0 0 a
0 c 0 0 c
b a 0 0 c
b c 0 0 a
a 0 0 0 a
a b 0 0 c
c 0 0 0 c
c b 0 0 a
a a 0 0 0
a c 0 0 b
c a 0 0 b
c c 0 0 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 9x2 + 6x3 + 0x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)3 (X_b)2 + (X_0)3 (X_b)2 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_a)2 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_c)2 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_a)2 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_c)2
Dual Codewords:
0 0 0 0 0
0 0 0 a 0
0 0 0 b 0
0 0 0 c 0
0 0 a 0 0
0 0 a a 0
0 0 a b 0
0 0 a c 0
0 0 b 0 0
0 0 b a 0
0 0 b b 0
0 0 b c 0
0 0 c 0 0
0 0 c a 0
0 0 c b 0
0 0 c c 0
Is it a nice code?: No
Generator Matrix-11
a 0 0 0 a
0 a 0 a 0
b 0 0 0 b
0 b 0 b 0
Codewords:
0 0 0 0 0
0 b 0 b 0
b 0 0 0 b
b b 0 b b
0 a 0 a 0
0 c 0 c 0
b a 0 a b
b c 0 c b
a 0 0 0 a
a b 0 b a
c 0 0 0 c
c b 0 b c
a a 0 a a
a c 0 c a
c a 0 a c
c c 0 c c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 6x2 + 0x3 + 9x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)3 (X_b)2 + (X_0)1 (X_b)4 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)1 (X_a)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)2 + (X_0)3 (X_a)2 + (X_0)1 (X_a)2 (X_b)2 + (X_0)3 (X_c)2 + (X_0)1 (X_b)2 (X_c)2 + (X_0)1 (X_a)4 + (X_0)1 (X_a)2 (X_c)2 + (X_0)1 (X_a)2 (X_c)2 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
0 0 a 0 0
0 0 b 0 0
0 0 c 0 0
Is it a nice code?: No
Generator Matrix-12
a 0 0 0 a
0 a 0 a a
b 0 0 0 b
0 b 0 b b
Codewords:
0 0 0 0 0
0 b 0 b b
b 0 0 0 b
b b 0 b 0
0 a 0 a a
0 c 0 c c
b a 0 a c
b c 0 c a
a 0 0 0 a
a b 0 b c
c 0 0 0 c
c b 0 b a
a a 0 a 0
a c 0 c b
c a 0 a b
c c 0 c 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)3 (X_a)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)3 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 a 0 0
0 0 b 0 0
0 0 c 0 0
Is it a nice code?: No
Generator Matrix-13
a 0 0 0 a
0 a a 0 0
b 0 0 0 b
0 b b 0 0
Codewords:
0 0 0 0 0
0 b b 0 0
b 0 0 0 b
b b b 0 b
0 a a 0 0
0 c c 0 0
b a a 0 b
b c c 0 b
a 0 0 0 a
a b b 0 a
c 0 0 0 c
c b b 0 c
a a a 0 a
a c c 0 a
c a a 0 c
c c c 0 c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 6x2 + 0x3 + 9x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)3 (X_b)2 + (X_0)1 (X_b)4 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)1 (X_a)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)2 + (X_0)3 (X_a)2 + (X_0)1 (X_a)2 (X_b)2 + (X_0)3 (X_c)2 + (X_0)1 (X_b)2 (X_c)2 + (X_0)1 (X_a)4 + (X_0)1 (X_a)2 (X_c)2 + (X_0)1 (X_a)2 (X_c)2 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
0 0 0 a 0
0 0 0 b 0
0 0 0 c 0
Is it a nice code?: No
Generator Matrix-14
a 0 0 0 a
0 a a 0 a
b 0 0 0 b
0 b b 0 b
Codewords:
0 0 0 0 0
0 b b 0 b
b 0 0 0 b
b b b 0 0
0 a a 0 a
0 c c 0 c
b a a 0 c
b c c 0 a
a 0 0 0 a
a b b 0 c
c 0 0 0 c
c b b 0 a
a a a 0 0
a c c 0 b
c a a 0 b
c c c 0 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)3 (X_a)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)3 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 0 a 0
0 0 0 b 0
0 0 0 c 0
Is it a nice code?: No
Generator Matrix-15
a 0 0 0 a
0 a a a 0
b 0 0 0 b
0 b b b 0
Codewords:
0 0 0 0 0
0 b b b 0
b 0 0 0 b
b b b b b
0 a a a 0
0 c c c 0
b a a a b
b c c c b
a 0 0 0 a
a b b b a
c 0 0 0 c
c b b b c
a a a a a
a c c c a
c a a a c
c c c c c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 3x3 + 0x4 + 9x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)3 (X_b)2 + (X_b)5 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_a)3 (X_b)2 + (X_b)2 (X_c)3 + (X_0)3 (X_a)2 + (X_a)2 (X_b)3 + (X_0)3 (X_c)2 + (X_b)3 (X_c)2 + (X_a)5 + (X_a)2 (X_c)3 + (X_a)3 (X_c)2 + (X_c)5
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-16
a 0 0 0 a
0 a a a a
b 0 0 0 b
0 b b b b
Codewords:
0 0 0 0 0
0 b b b b
b 0 0 0 b
b b b b 0
0 a a a a
0 c c c c
b a a a c
b c c c a
a 0 0 0 a
a b b b c
c 0 0 0 c
c b b b a
a a a a 0
a c c c b
c a a a b
c c c c 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3 + 6x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)1 (X_b)4 + (X_0)3 (X_b)2 + (X_0)1 (X_b)4 + (X_0)1 (X_a)4 + (X_0)1 (X_c)4 + (X_a)3 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)3 + (X_0)3 (X_a)2 + (X_a)1 (X_b)3 (X_c)1 + (X_0)3 (X_c)2 + (X_a)1 (X_b)3 (X_c)1 + (X_0)1 (X_a)4 + (X_a)1 (X_b)1 (X_c)3 + (X_a)3 (X_b)1 (X_c)1 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-17
a 0 0 a 0
0 a 0 0 0
b 0 0 b 0
0 b 0 0 0
Codewords:
0 0 0 0 0
0 b 0 0 0
b 0 0 b 0
b b 0 b 0
0 a 0 0 0
0 c 0 0 0
b a 0 b 0
b c 0 b 0
a 0 0 a 0
a b 0 a 0
c 0 0 c 0
c b 0 c 0
a a 0 a 0
a c 0 a 0
c a 0 c 0
c c 0 c 0
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 3x2 + 9x3 + 0x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)4 (X_b)1 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)4 (X_a)1 + (X_0)4 (X_c)1 + (X_0)2 (X_a)1 (X_b)2 + (X_0)2 (X_b)2 (X_c)1 + (X_0)3 (X_a)2 + (X_0)2 (X_a)2 (X_b)1 + (X_0)3 (X_c)2 + (X_0)2 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_0)2 (X_a)2 (X_c)1 + (X_0)2 (X_a)1 (X_c)2 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
0 0 a 0 0
0 0 a 0 a
0 0 a 0 b
0 0 a 0 c
0 0 b 0 0
0 0 b 0 a
0 0 b 0 b
0 0 b 0 c
0 0 c 0 0
0 0 c 0 a
0 0 c 0 b
0 0 c 0 c
Is it a nice code?: No
Generator Matrix-18
a 0 0 a 0
0 a 0 0 a
b 0 0 b 0
0 b 0 0 b
Codewords:
0 0 0 0 0
0 b 0 0 b
b 0 0 b 0
b b 0 b b
0 a 0 0 a
0 c 0 0 c
b a 0 b a
b c 0 b c
a 0 0 a 0
a b 0 a b
c 0 0 c 0
c b 0 c b
a a 0 a a
a c 0 a c
c a 0 c a
c c 0 c c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 6x2 + 0x3 + 9x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)3 (X_b)2 + (X_0)1 (X_b)4 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)1 (X_a)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)2 + (X_0)3 (X_a)2 + (X_0)1 (X_a)2 (X_b)2 + (X_0)3 (X_c)2 + (X_0)1 (X_b)2 (X_c)2 + (X_0)1 (X_a)4 + (X_0)1 (X_a)2 (X_c)2 + (X_0)1 (X_a)2 (X_c)2 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
0 0 a 0 0
0 0 b 0 0
0 0 c 0 0
Is it a nice code?: No
Generator Matrix-19
a 0 0 a 0
0 a 0 a 0
b 0 0 b 0
0 b 0 b 0
Codewords:
0 0 0 0 0
0 b 0 b 0
b 0 0 b 0
b b 0 0 0
0 a 0 a 0
0 c 0 c 0
b a 0 c 0
b c 0 a 0
a 0 0 a 0
a b 0 c 0
c 0 0 c 0
c b 0 a 0
a a 0 0 0
a c 0 b 0
c a 0 b 0
c c 0 0 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 9x2 + 6x3 + 0x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)3 (X_b)2 + (X_0)3 (X_b)2 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_a)2 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_c)2 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_a)2 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_c)2
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
0 0 a 0 0
0 0 a 0 a
0 0 a 0 b
0 0 a 0 c
0 0 b 0 0
0 0 b 0 a
0 0 b 0 b
0 0 b 0 c
0 0 c 0 0
0 0 c 0 a
0 0 c 0 b
0 0 c 0 c
Is it a nice code?: No
Generator Matrix-20
a 0 0 a 0
0 a 0 a a
b 0 0 b 0
0 b 0 b b
Codewords:
0 0 0 0 0
0 b 0 b b
b 0 0 b 0
b b 0 0 b
0 a 0 a a
0 c 0 c c
b a 0 c a
b c 0 a c
a 0 0 a 0
a b 0 c b
c 0 0 c 0
c b 0 a b
a a 0 0 a
a c 0 b c
c a 0 b a
c c 0 0 c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)3 (X_a)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)3 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 a 0 0
0 0 b 0 0
0 0 c 0 0
Is it a nice code?: No
Generator Matrix-21
a 0 0 a 0
0 a a 0 0
b 0 0 b 0
0 b b 0 0
Codewords:
0 0 0 0 0
0 b b 0 0
b 0 0 b 0
b b b b 0
0 a a 0 0
0 c c 0 0
b a a b 0
b c c b 0
a 0 0 a 0
a b b a 0
c 0 0 c 0
c b b c 0
a a a a 0
a c c a 0
c a a c 0
c c c c 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 6x2 + 0x3 + 9x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)3 (X_b)2 + (X_0)1 (X_b)4 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)1 (X_a)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)2 + (X_0)3 (X_a)2 + (X_0)1 (X_a)2 (X_b)2 + (X_0)3 (X_c)2 + (X_0)1 (X_b)2 (X_c)2 + (X_0)1 (X_a)4 + (X_0)1 (X_a)2 (X_c)2 + (X_0)1 (X_a)2 (X_c)2 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
Is it a nice code?: No
Generator Matrix-22
a 0 0 a 0
0 a a 0 a
b 0 0 b 0
0 b b 0 b
Codewords:
0 0 0 0 0
0 b b 0 b
b 0 0 b 0
b b b b b
0 a a 0 a
0 c c 0 c
b a a b a
b c c b c
a 0 0 a 0
a b b a b
c 0 0 c 0
c b b c b
a a a a a
a c c a c
c a a c a
c c c c c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 3x3 + 0x4 + 9x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)3 (X_b)2 + (X_b)5 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_a)3 (X_b)2 + (X_b)2 (X_c)3 + (X_0)3 (X_a)2 + (X_a)2 (X_b)3 + (X_0)3 (X_c)2 + (X_b)3 (X_c)2 + (X_a)5 + (X_a)2 (X_c)3 + (X_a)3 (X_c)2 + (X_c)5
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-23
a 0 0 a 0
0 a a a 0
b 0 0 b 0
0 b b b 0
Codewords:
0 0 0 0 0
0 b b b 0
b 0 0 b 0
b b b 0 0
0 a a a 0
0 c c c 0
b a a c 0
b c c a 0
a 0 0 a 0
a b b c 0
c 0 0 c 0
c b b a 0
a a a 0 0
a c c b 0
c a a b 0
c c c 0 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)3 (X_a)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)3 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
Is it a nice code?: No
Generator Matrix-24
a 0 0 a 0
0 a a a a
b 0 0 b 0
0 b b b b
Codewords:
0 0 0 0 0
0 b b b b
b 0 0 b 0
b b b 0 b
0 a a a a
0 c c c c
b a a c a
b c c a c
a 0 0 a 0
a b b c b
c 0 0 c 0
c b b a b
a a a 0 a
a c c b c
c a a b a
c c c 0 c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3 + 6x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)1 (X_b)4 + (X_0)3 (X_b)2 + (X_0)1 (X_b)4 + (X_0)1 (X_a)4 + (X_0)1 (X_c)4 + (X_a)3 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)3 + (X_0)3 (X_a)2 + (X_a)1 (X_b)3 (X_c)1 + (X_0)3 (X_c)2 + (X_a)1 (X_b)3 (X_c)1 + (X_0)1 (X_a)4 + (X_a)1 (X_b)1 (X_c)3 + (X_a)3 (X_b)1 (X_c)1 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-25
a 0 0 a a
0 a 0 0 0
b 0 0 b b
0 b 0 0 0
Codewords:
0 0 0 0 0
0 b 0 0 0
b 0 0 b b
b b 0 b b
0 a 0 0 0
0 c 0 0 0
b a 0 b b
b c 0 b b
a 0 0 a a
a b 0 a a
c 0 0 c c
c b 0 c c
a a 0 a a
a c 0 a a
c a 0 c c
c c 0 c c
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 0x2 + 3x3 + 9x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)4 (X_b)1 + (X_0)2 (X_b)3 + (X_0)1 (X_b)4 + (X_0)4 (X_a)1 + (X_0)4 (X_c)1 + (X_0)1 (X_a)1 (X_b)3 + (X_0)1 (X_b)3 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)3 (X_b)1 + (X_0)2 (X_c)3 + (X_0)1 (X_b)1 (X_c)3 + (X_0)1 (X_a)4 + (X_0)1 (X_a)3 (X_c)1 + (X_0)1 (X_a)1 (X_c)3 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
0 0 a 0 0
0 0 b 0 0
0 0 c 0 0
Is it a nice code?: No
Generator Matrix-26
a 0 0 a a
0 a 0 0 a
b 0 0 b b
0 b 0 0 b
Codewords:
0 0 0 0 0
0 b 0 0 b
b 0 0 b b
b b 0 b 0
0 a 0 0 a
0 c 0 0 c
b a 0 b c
b c 0 b a
a 0 0 a a
a b 0 a c
c 0 0 c c
c b 0 c a
a a 0 a 0
a c 0 a b
c a 0 c b
c c 0 c 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 a 0 0
0 0 b 0 0
0 0 c 0 0
Is it a nice code?: No
Generator Matrix-27
a 0 0 a a
0 a 0 a 0
b 0 0 b b
0 b 0 b 0
Codewords:
0 0 0 0 0
0 b 0 b 0
b 0 0 b b
b b 0 0 b
0 a 0 a 0
0 c 0 c 0
b a 0 c b
b c 0 a b
a 0 0 a a
a b 0 c a
c 0 0 c c
c b 0 a c
a a 0 0 a
a c 0 b a
c a 0 b c
c c 0 0 c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 a 0 0
0 0 b 0 0
0 0 c 0 0
Is it a nice code?: No
Generator Matrix-28
a 0 0 a a
0 a 0 a a
b 0 0 b b
0 b 0 b b
Codewords:
0 0 0 0 0
0 b 0 b b
b 0 0 b b
b b 0 0 0
0 a 0 a a
0 c 0 c c
b a 0 c c
b c 0 a a
a 0 0 a a
a b 0 c c
c 0 0 c c
c b 0 a a
a a 0 0 0
a c 0 b b
c a 0 b b
c c 0 0 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)3 (X_b)2 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_c)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)3 (X_a)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)3 (X_c)2
Dual Codewords:
0 0 0 0 0
0 0 a 0 0
0 0 b 0 0
0 0 c 0 0
Is it a nice code?: No
Generator Matrix-29
a 0 0 a a
0 a a 0 0
b 0 0 b b
0 b b 0 0
Codewords:
0 0 0 0 0
0 b b 0 0
b 0 0 b b
b b b b b
0 a a 0 0
0 c c 0 0
b a a b b
b c c b b
a 0 0 a a
a b b a a
c 0 0 c c
c b b c c
a a a a a
a c c a a
c a a c c
c c c c c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 3x3 + 0x4 + 9x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_b)5 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_a)2 (X_b)3 + (X_b)3 (X_c)2 + (X_0)2 (X_a)3 + (X_a)3 (X_b)2 + (X_0)2 (X_c)3 + (X_b)2 (X_c)3 + (X_a)5 + (X_a)3 (X_c)2 + (X_a)2 (X_c)3 + (X_c)5
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-30
a 0 0 a a
0 a a 0 a
b 0 0 b b
0 b b 0 b
Codewords:
0 0 0 0 0
0 b b 0 b
b 0 0 b b
b b b b 0
0 a a 0 a
0 c c 0 c
b a a b c
b c c b a
a 0 0 a a
a b b a c
c 0 0 c c
c b b c a
a a a a 0
a c c a b
c a a c b
c c c c 0
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 6x3 + 3x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)1 (X_b)4 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_a)2 (X_b)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)2 + (X_0)2 (X_a)3 + (X_a)2 (X_b)2 (X_c)1 + (X_0)2 (X_c)3 + (X_a)1 (X_b)2 (X_c)2 + (X_0)1 (X_a)4 + (X_a)2 (X_b)1 (X_c)2 + (X_a)2 (X_b)1 (X_c)2 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-31
a 0 0 a a
0 a a a 0
b 0 0 b b
0 b b b 0
Codewords:
0 0 0 0 0
0 b b b 0
b 0 0 b b
b b b 0 b
0 a a a 0
0 c c c 0
b a a c b
b c c a b
a 0 0 a a
a b b c a
c 0 0 c c
c b b a c
a a a 0 a
a c c b a
c a a b c
c c c 0 c
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 6x3 + 3x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)1 (X_b)4 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_a)2 (X_b)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)2 + (X_0)2 (X_a)3 + (X_a)2 (X_b)2 (X_c)1 + (X_0)2 (X_c)3 + (X_a)1 (X_b)2 (X_c)2 + (X_0)1 (X_a)4 + (X_a)2 (X_b)1 (X_c)2 + (X_a)2 (X_b)1 (X_c)2 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-32
a 0 0 a a
0 a a a a
b 0 0 b b
0 b b b b
Codewords:
0 0 0 0 0
0 b b b b
b 0 0 b b
b b b 0 0
0 a a a a
0 c c c c
b a a c c
b c c a a
a 0 0 a a
a b b c c
c 0 0 c c
c b b a a
a a a 0 0
a c c b b
c a a b b
c c c 0 0
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 6x3 + 3x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)1 (X_b)4 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)1 (X_a)4 + (X_0)1 (X_c)4 + (X_a)2 (X_b)1 (X_c)2 + (X_a)2 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_a)1 (X_b)2 (X_c)2 + (X_0)2 (X_c)3 + (X_a)2 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_a)1 (X_b)2 (X_c)2 + (X_a)2 (X_b)2 (X_c)1 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-33
a 0 a 0 0
0 a 0 0 0
b 0 b 0 0
0 b 0 0 0
Codewords:
0 0 0 0 0
0 b 0 0 0
b 0 b 0 0
b b b 0 0
0 a 0 0 0
0 c 0 0 0
b a b 0 0
b c b 0 0
a 0 a 0 0
a b a 0 0
c 0 c 0 0
c b c 0 0
a a a 0 0
a c a 0 0
c a c 0 0
c c c 0 0
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 3x2 + 9x3 + 0x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)4 (X_b)1 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)4 (X_a)1 + (X_0)4 (X_c)1 + (X_0)2 (X_a)1 (X_b)2 + (X_0)2 (X_b)2 (X_c)1 + (X_0)3 (X_a)2 + (X_0)2 (X_a)2 (X_b)1 + (X_0)3 (X_c)2 + (X_0)2 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_0)2 (X_a)2 (X_c)1 + (X_0)2 (X_a)1 (X_c)2 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
0 0 0 a 0
0 0 0 a a
0 0 0 a b
0 0 0 a c
0 0 0 b 0
0 0 0 b a
0 0 0 b b
0 0 0 b c
0 0 0 c 0
0 0 0 c a
0 0 0 c b
0 0 0 c c
Is it a nice code?: No
Generator Matrix-34
a 0 a 0 0
0 a 0 0 a
b 0 b 0 0
0 b 0 0 b
Codewords:
0 0 0 0 0
0 b 0 0 b
b 0 b 0 0
b b b 0 b
0 a 0 0 a
0 c 0 0 c
b a b 0 a
b c b 0 c
a 0 a 0 0
a b a 0 b
c 0 c 0 0
c b c 0 b
a a a 0 a
a c a 0 c
c a c 0 a
c c c 0 c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 6x2 + 0x3 + 9x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)3 (X_b)2 + (X_0)1 (X_b)4 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)1 (X_a)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)2 + (X_0)3 (X_a)2 + (X_0)1 (X_a)2 (X_b)2 + (X_0)3 (X_c)2 + (X_0)1 (X_b)2 (X_c)2 + (X_0)1 (X_a)4 + (X_0)1 (X_a)2 (X_c)2 + (X_0)1 (X_a)2 (X_c)2 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
0 0 0 a 0
0 0 0 b 0
0 0 0 c 0
Is it a nice code?: No
Generator Matrix-35
a 0 a 0 0
0 a 0 a 0
b 0 b 0 0
0 b 0 b 0
Codewords:
0 0 0 0 0
0 b 0 b 0
b 0 b 0 0
b b b b 0
0 a 0 a 0
0 c 0 c 0
b a b a 0
b c b c 0
a 0 a 0 0
a b a b 0
c 0 c 0 0
c b c b 0
a a a a 0
a c a c 0
c a c a 0
c c c c 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 6x2 + 0x3 + 9x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)3 (X_b)2 + (X_0)1 (X_b)4 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)1 (X_a)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)2 + (X_0)3 (X_a)2 + (X_0)1 (X_a)2 (X_b)2 + (X_0)3 (X_c)2 + (X_0)1 (X_b)2 (X_c)2 + (X_0)1 (X_a)4 + (X_0)1 (X_a)2 (X_c)2 + (X_0)1 (X_a)2 (X_c)2 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
Is it a nice code?: No
Generator Matrix-36
a 0 a 0 0
0 a 0 a a
b 0 b 0 0
0 b 0 b b
Codewords:
0 0 0 0 0
0 b 0 b b
b 0 b 0 0
b b b b b
0 a 0 a a
0 c 0 c c
b a b a a
b c b c c
a 0 a 0 0
a b a b b
c 0 c 0 0
c b c b b
a a a a a
a c a c c
c a c a a
c c c c c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 3x3 + 0x4 + 9x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)3 (X_b)2 + (X_b)5 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_a)3 (X_b)2 + (X_b)2 (X_c)3 + (X_0)3 (X_a)2 + (X_a)2 (X_b)3 + (X_0)3 (X_c)2 + (X_b)3 (X_c)2 + (X_a)5 + (X_a)2 (X_c)3 + (X_a)3 (X_c)2 + (X_c)5
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-37
a 0 a 0 0
0 a a 0 0
b 0 b 0 0
0 b b 0 0
Codewords:
0 0 0 0 0
0 b b 0 0
b 0 b 0 0
b b 0 0 0
0 a a 0 0
0 c c 0 0
b a c 0 0
b c a 0 0
a 0 a 0 0
a b c 0 0
c 0 c 0 0
c b a 0 0
a a 0 0 0
a c b 0 0
c a b 0 0
c c 0 0 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 9x2 + 6x3 + 0x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)3 (X_b)2 + (X_0)3 (X_b)2 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_a)2 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_c)2 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_a)2 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_c)2
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
0 0 0 a 0
0 0 0 a a
0 0 0 a b
0 0 0 a c
0 0 0 b 0
0 0 0 b a
0 0 0 b b
0 0 0 b c
0 0 0 c 0
0 0 0 c a
0 0 0 c b
0 0 0 c c
Is it a nice code?: No
Generator Matrix-38
a 0 a 0 0
0 a a 0 a
b 0 b 0 0
0 b b 0 b
Codewords:
0 0 0 0 0
0 b b 0 b
b 0 b 0 0
b b 0 0 b
0 a a 0 a
0 c c 0 c
b a c 0 a
b c a 0 c
a 0 a 0 0
a b c 0 b
c 0 c 0 0
c b a 0 b
a a 0 0 a
a c b 0 c
c a b 0 a
c c 0 0 c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)3 (X_a)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)3 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 0 a 0
0 0 0 b 0
0 0 0 c 0
Is it a nice code?: No
Generator Matrix-39
a 0 a 0 0
0 a a a 0
b 0 b 0 0
0 b b b 0
Codewords:
0 0 0 0 0
0 b b b 0
b 0 b 0 0
b b 0 b 0
0 a a a 0
0 c c c 0
b a c a 0
b c a c 0
a 0 a 0 0
a b c b 0
c 0 c 0 0
c b a b 0
a a 0 a 0
a c b c 0
c a b a 0
c c 0 c 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)3 (X_a)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)3 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
Is it a nice code?: No
Generator Matrix-40
a 0 a 0 0
0 a a a a
b 0 b 0 0
0 b b b b
Codewords:
0 0 0 0 0
0 b b b b
b 0 b 0 0
b b 0 b b
0 a a a a
0 c c c c
b a c a a
b c a c c
a 0 a 0 0
a b c b b
c 0 c 0 0
c b a b b
a a 0 a a
a c b c c
c a b a a
c c 0 c c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3 + 6x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)1 (X_b)4 + (X_0)3 (X_b)2 + (X_0)1 (X_b)4 + (X_0)1 (X_a)4 + (X_0)1 (X_c)4 + (X_a)3 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)3 + (X_0)3 (X_a)2 + (X_a)1 (X_b)3 (X_c)1 + (X_0)3 (X_c)2 + (X_a)1 (X_b)3 (X_c)1 + (X_0)1 (X_a)4 + (X_a)1 (X_b)1 (X_c)3 + (X_a)3 (X_b)1 (X_c)1 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-41
a 0 a 0 a
0 a 0 0 0
b 0 b 0 b
0 b 0 0 0
Codewords:
0 0 0 0 0
0 b 0 0 0
b 0 b 0 b
b b b 0 b
0 a 0 0 0
0 c 0 0 0
b a b 0 b
b c b 0 b
a 0 a 0 a
a b a 0 a
c 0 c 0 c
c b c 0 c
a a a 0 a
a c a 0 a
c a c 0 c
c c c 0 c
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 0x2 + 3x3 + 9x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)4 (X_b)1 + (X_0)2 (X_b)3 + (X_0)1 (X_b)4 + (X_0)4 (X_a)1 + (X_0)4 (X_c)1 + (X_0)1 (X_a)1 (X_b)3 + (X_0)1 (X_b)3 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)3 (X_b)1 + (X_0)2 (X_c)3 + (X_0)1 (X_b)1 (X_c)3 + (X_0)1 (X_a)4 + (X_0)1 (X_a)3 (X_c)1 + (X_0)1 (X_a)1 (X_c)3 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
0 0 0 a 0
0 0 0 b 0
0 0 0 c 0
Is it a nice code?: No
Generator Matrix-42
a 0 a 0 a
0 a 0 0 a
b 0 b 0 b
0 b 0 0 b
Codewords:
0 0 0 0 0
0 b 0 0 b
b 0 b 0 b
b b b 0 0
0 a 0 0 a
0 c 0 0 c
b a b 0 c
b c b 0 a
a 0 a 0 a
a b a 0 c
c 0 c 0 c
c b c 0 a
a a a 0 0
a c a 0 b
c a c 0 b
c c c 0 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 0 a 0
0 0 0 b 0
0 0 0 c 0
Is it a nice code?: No
Generator Matrix-43
a 0 a 0 a
0 a 0 a 0
b 0 b 0 b
0 b 0 b 0
Codewords:
0 0 0 0 0
0 b 0 b 0
b 0 b 0 b
b b b b b
0 a 0 a 0
0 c 0 c 0
b a b a b
b c b c b
a 0 a 0 a
a b a b a
c 0 c 0 c
c b c b c
a a a a a
a c a c a
c a c a c
c c c c c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 3x3 + 0x4 + 9x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_b)5 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_a)2 (X_b)3 + (X_b)3 (X_c)2 + (X_0)2 (X_a)3 + (X_a)3 (X_b)2 + (X_0)2 (X_c)3 + (X_b)2 (X_c)3 + (X_a)5 + (X_a)3 (X_c)2 + (X_a)2 (X_c)3 + (X_c)5
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-44
a 0 a 0 a
0 a 0 a a
b 0 b 0 b
0 b 0 b b
Codewords:
0 0 0 0 0
0 b 0 b b
b 0 b 0 b
b b b b 0
0 a 0 a a
0 c 0 c c
b a b a c
b c b c a
a 0 a 0 a
a b a b c
c 0 c 0 c
c b c b a
a a a a 0
a c a c b
c a c a b
c c c c 0
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 6x3 + 3x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)1 (X_b)4 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_a)2 (X_b)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)2 + (X_0)2 (X_a)3 + (X_a)2 (X_b)2 (X_c)1 + (X_0)2 (X_c)3 + (X_a)1 (X_b)2 (X_c)2 + (X_0)1 (X_a)4 + (X_a)2 (X_b)1 (X_c)2 + (X_a)2 (X_b)1 (X_c)2 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-45
a 0 a 0 a
0 a a 0 0
b 0 b 0 b
0 b b 0 0
Codewords:
0 0 0 0 0
0 b b 0 0
b 0 b 0 b
b b 0 0 b
0 a a 0 0
0 c c 0 0
b a c 0 b
b c a 0 b
a 0 a 0 a
a b c 0 a
c 0 c 0 c
c b a 0 c
a a 0 0 a
a c b 0 a
c a b 0 c
c c 0 0 c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 0 a 0
0 0 0 b 0
0 0 0 c 0
Is it a nice code?: No
Generator Matrix-46
a 0 a 0 a
0 a a 0 a
b 0 b 0 b
0 b b 0 b
Codewords:
0 0 0 0 0
0 b b 0 b
b 0 b 0 b
b b 0 0 0
0 a a 0 a
0 c c 0 c
b a c 0 c
b c a 0 a
a 0 a 0 a
a b c 0 c
c 0 c 0 c
c b a 0 a
a a 0 0 0
a c b 0 b
c a b 0 b
c c 0 0 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)3 (X_b)2 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_c)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)3 (X_a)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)3 (X_c)2
Dual Codewords:
0 0 0 0 0
0 0 0 a 0
0 0 0 b 0
0 0 0 c 0
Is it a nice code?: No
Generator Matrix-47
a 0 a 0 a
0 a a a 0
b 0 b 0 b
0 b b b 0
Codewords:
0 0 0 0 0
0 b b b 0
b 0 b 0 b
b b 0 b b
0 a a a 0
0 c c c 0
b a c a b
b c a c b
a 0 a 0 a
a b c b a
c 0 c 0 c
c b a b c
a a 0 a a
a c b c a
c a b a c
c c 0 c c
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 6x3 + 3x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)1 (X_b)4 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_a)2 (X_b)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)2 + (X_0)2 (X_a)3 + (X_a)2 (X_b)2 (X_c)1 + (X_0)2 (X_c)3 + (X_a)1 (X_b)2 (X_c)2 + (X_0)1 (X_a)4 + (X_a)2 (X_b)1 (X_c)2 + (X_a)2 (X_b)1 (X_c)2 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-48
a 0 a 0 a
0 a a a a
b 0 b 0 b
0 b b b b
Codewords:
0 0 0 0 0
0 b b b b
b 0 b 0 b
b b 0 b 0
0 a a a a
0 c c c c
b a c a c
b c a c a
a 0 a 0 a
a b c b c
c 0 c 0 c
c b a b a
a a 0 a 0
a c b c b
c a b a b
c c 0 c 0
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 6x3 + 3x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)1 (X_b)4 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)1 (X_a)4 + (X_0)1 (X_c)4 + (X_a)2 (X_b)1 (X_c)2 + (X_a)2 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_a)1 (X_b)2 (X_c)2 + (X_0)2 (X_c)3 + (X_a)2 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_a)1 (X_b)2 (X_c)2 + (X_a)2 (X_b)2 (X_c)1 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-49
a 0 a a 0
0 a 0 0 0
b 0 b b 0
0 b 0 0 0
Codewords:
0 0 0 0 0
0 b 0 0 0
b 0 b b 0
b b b b 0
0 a 0 0 0
0 c 0 0 0
b a b b 0
b c b b 0
a 0 a a 0
a b a a 0
c 0 c c 0
c b c c 0
a a a a 0
a c a a 0
c a c c 0
c c c c 0
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 0x2 + 3x3 + 9x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)4 (X_b)1 + (X_0)2 (X_b)3 + (X_0)1 (X_b)4 + (X_0)4 (X_a)1 + (X_0)4 (X_c)1 + (X_0)1 (X_a)1 (X_b)3 + (X_0)1 (X_b)3 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)3 (X_b)1 + (X_0)2 (X_c)3 + (X_0)1 (X_b)1 (X_c)3 + (X_0)1 (X_a)4 + (X_0)1 (X_a)3 (X_c)1 + (X_0)1 (X_a)1 (X_c)3 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
Is it a nice code?: No
Generator Matrix-50
a 0 a a 0
0 a 0 0 a
b 0 b b 0
0 b 0 0 b
Codewords:
0 0 0 0 0
0 b 0 0 b
b 0 b b 0
b b b b b
0 a 0 0 a
0 c 0 0 c
b a b b a
b c b b c
a 0 a a 0
a b a a b
c 0 c c 0
c b c c b
a a a a a
a c a a c
c a c c a
c c c c c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 3x3 + 0x4 + 9x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_b)5 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_a)2 (X_b)3 + (X_b)3 (X_c)2 + (X_0)2 (X_a)3 + (X_a)3 (X_b)2 + (X_0)2 (X_c)3 + (X_b)2 (X_c)3 + (X_a)5 + (X_a)3 (X_c)2 + (X_a)2 (X_c)3 + (X_c)5
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-51
a 0 a a 0
0 a 0 a 0
b 0 b b 0
0 b 0 b 0
Codewords:
0 0 0 0 0
0 b 0 b 0
b 0 b b 0
b b b 0 0
0 a 0 a 0
0 c 0 c 0
b a b c 0
b c b a 0
a 0 a a 0
a b a c 0
c 0 c c 0
c b c a 0
a a a 0 0
a c a b 0
c a c b 0
c c c 0 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
Is it a nice code?: No
Generator Matrix-52
a 0 a a 0
0 a 0 a a
b 0 b b 0
0 b 0 b b
Codewords:
0 0 0 0 0
0 b 0 b b
b 0 b b 0
b b b 0 b
0 a 0 a a
0 c 0 c c
b a b c a
b c b a c
a 0 a a 0
a b a c b
c 0 c c 0
c b c a b
a a a 0 a
a c a b c
c a c b a
c c c 0 c
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 6x3 + 3x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)1 (X_b)4 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_a)2 (X_b)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)2 + (X_0)2 (X_a)3 + (X_a)2 (X_b)2 (X_c)1 + (X_0)2 (X_c)3 + (X_a)1 (X_b)2 (X_c)2 + (X_0)1 (X_a)4 + (X_a)2 (X_b)1 (X_c)2 + (X_a)2 (X_b)1 (X_c)2 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-53
a 0 a a 0
0 a a 0 0
b 0 b b 0
0 b b 0 0
Codewords:
0 0 0 0 0
0 b b 0 0
b 0 b b 0
b b 0 b 0
0 a a 0 0
0 c c 0 0
b a c b 0
b c a b 0
a 0 a a 0
a b c a 0
c 0 c c 0
c b a c 0
a a 0 a 0
a c b a 0
c a b c 0
c c 0 c 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
Is it a nice code?: No
Generator Matrix-54
a 0 a a 0
0 a a 0 a
b 0 b b 0
0 b b 0 b
Codewords:
0 0 0 0 0
0 b b 0 b
b 0 b b 0
b b 0 b b
0 a a 0 a
0 c c 0 c
b a c b a
b c a b c
a 0 a a 0
a b c a b
c 0 c c 0
c b a c b
a a 0 a a
a c b a c
c a b c a
c c 0 c c
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 6x3 + 3x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)1 (X_b)4 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_a)2 (X_b)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)2 + (X_0)2 (X_a)3 + (X_a)2 (X_b)2 (X_c)1 + (X_0)2 (X_c)3 + (X_a)1 (X_b)2 (X_c)2 + (X_0)1 (X_a)4 + (X_a)2 (X_b)1 (X_c)2 + (X_a)2 (X_b)1 (X_c)2 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-55
a 0 a a 0
0 a a a 0
b 0 b b 0
0 b b b 0
Codewords:
0 0 0 0 0
0 b b b 0
b 0 b b 0
b b 0 0 0
0 a a a 0
0 c c c 0
b a c c 0
b c a a 0
a 0 a a 0
a b c c 0
c 0 c c 0
c b a a 0
a a 0 0 0
a c b b 0
c a b b 0
c c 0 0 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 6x3 + 6x4 + 0x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)3 (X_b)2 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_a)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_c)3 + (X_0)1 (X_a)2 (X_b)1 (X_c)1 + (X_0)3 (X_a)2 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 (X_c)1 + (X_0)3 (X_c)2
Dual Codewords:
0 0 0 0 0
0 0 0 0 a
0 0 0 0 b
0 0 0 0 c
Is it a nice code?: No
Generator Matrix-56
a 0 a a 0
0 a a a a
b 0 b b 0
0 b b b b
Codewords:
0 0 0 0 0
0 b b b b
b 0 b b 0
b b 0 0 b
0 a a a a
0 c c c c
b a c c a
b c a a c
a 0 a a 0
a b c c b
c 0 c c 0
c b a a b
a a 0 0 a
a c b b c
c a b b a
c c 0 0 c
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 6x3 + 3x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)1 (X_b)4 + (X_0)2 (X_b)3 + (X_0)2 (X_b)3 + (X_0)1 (X_a)4 + (X_0)1 (X_c)4 + (X_a)2 (X_b)1 (X_c)2 + (X_a)2 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_a)1 (X_b)2 (X_c)2 + (X_0)2 (X_c)3 + (X_a)2 (X_b)2 (X_c)1 + (X_0)2 (X_a)3 + (X_a)1 (X_b)2 (X_c)2 + (X_a)2 (X_b)2 (X_c)1 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-57
a 0 a a a
0 a 0 0 0
b 0 b b b
0 b 0 0 0
Codewords:
0 0 0 0 0
0 b 0 0 0
b 0 b b b
b b b b b
0 a 0 0 0
0 c 0 0 0
b a b b b
b c b b b
a 0 a a a
a b a a a
c 0 c c c
c b c c c
a a a a a
a c a a a
c a c c c
c c c c c
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 0x2 + 0x3 + 3x4 + 9x5
Complete Weight Enumerator: (X_0)5 + (X_0)4 (X_b)1 + (X_0)1 (X_b)4 + (X_b)5 + (X_0)4 (X_a)1 + (X_0)4 (X_c)1 + (X_a)1 (X_b)4 + (X_b)4 (X_c)1 + (X_0)1 (X_a)4 + (X_a)4 (X_b)1 + (X_0)1 (X_c)4 + (X_b)1 (X_c)4 + (X_a)5 + (X_a)4 (X_c)1 + (X_a)1 (X_c)4 + (X_c)5
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-58
a 0 a a a
0 a 0 0 a
b 0 b b b
0 b 0 0 b
Codewords:
0 0 0 0 0
0 b 0 0 b
b 0 b b b
b b b b 0
0 a 0 0 a
0 c 0 0 c
b a b b c
b c b b a
a 0 a a a
a b a a c
c 0 c c c
c b c c a
a a a a 0
a c a a b
c a c c b
c c c c 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3 + 6x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)1 (X_b)4 + (X_0)1 (X_b)4 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_a)1 (X_b)3 (X_c)1 + (X_a)1 (X_b)3 (X_c)1 + (X_0)1 (X_a)4 + (X_a)3 (X_b)1 (X_c)1 + (X_0)1 (X_c)4 + (X_a)1 (X_b)1 (X_c)3 + (X_0)1 (X_a)4 + (X_a)3 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)3 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-59
a 0 a a a
0 a 0 a 0
b 0 b b b
0 b 0 b 0
Codewords:
0 0 0 0 0
0 b 0 b 0
b 0 b b b
b b b 0 b
0 a 0 a 0
0 c 0 c 0
b a b c b
b c b a b
a 0 a a a
a b a c a
c 0 c c c
c b c a c
a a a 0 a
a c a b a
c a c b c
c c c 0 c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3 + 6x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)1 (X_b)4 + (X_0)1 (X_b)4 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_a)1 (X_b)3 (X_c)1 + (X_a)1 (X_b)3 (X_c)1 + (X_0)1 (X_a)4 + (X_a)3 (X_b)1 (X_c)1 + (X_0)1 (X_c)4 + (X_a)1 (X_b)1 (X_c)3 + (X_0)1 (X_a)4 + (X_a)3 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)3 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-60
a 0 a a a
0 a 0 a a
b 0 b b b
0 b 0 b b
Codewords:
0 0 0 0 0
0 b 0 b b
b 0 b b b
b b b 0 0
0 a 0 a a
0 c 0 c c
b a b c c
b c b a a
a 0 a a a
a b a c c
c 0 c c c
c b c a a
a a a 0 0
a c a b b
c a c b b
c c c 0 0
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 6x3 + 3x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)1 (X_b)4 + (X_0)2 (X_b)3 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_a)1 (X_b)2 (X_c)2 + (X_a)2 (X_b)2 (X_c)1 + (X_0)1 (X_a)4 + (X_a)2 (X_b)1 (X_c)2 + (X_0)1 (X_c)4 + (X_a)2 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_a)2 (X_b)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)2 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-61
a 0 a a a
0 a a 0 0
b 0 b b b
0 b b 0 0
Codewords:
0 0 0 0 0
0 b b 0 0
b 0 b b b
b b 0 b b
0 a a 0 0
0 c c 0 0
b a c b b
b c a b b
a 0 a a a
a b c a a
c 0 c c c
c b a c c
a a 0 a a
a c b a a
c a b c c
c c 0 c c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3 + 6x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)3 (X_b)2 + (X_0)1 (X_b)4 + (X_0)1 (X_b)4 + (X_0)3 (X_a)2 + (X_0)3 (X_c)2 + (X_a)1 (X_b)3 (X_c)1 + (X_a)1 (X_b)3 (X_c)1 + (X_0)1 (X_a)4 + (X_a)3 (X_b)1 (X_c)1 + (X_0)1 (X_c)4 + (X_a)1 (X_b)1 (X_c)3 + (X_0)1 (X_a)4 + (X_a)3 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)3 + (X_0)1 (X_c)4
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-62
a 0 a a a
0 a a 0 a
b 0 b b b
0 b b 0 b
Codewords:
0 0 0 0 0
0 b b 0 b
b 0 b b b
b b 0 b 0
0 a a 0 a
0 c c 0 c
b a c b c
b c a b a
a 0 a a a
a b c a c
c 0 c c c
c b a c a
a a 0 a 0
a c b a b
c a b c b
c c 0 c 0
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 6x3 + 3x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)1 (X_b)4 + (X_0)2 (X_b)3 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_a)1 (X_b)2 (X_c)2 + (X_a)2 (X_b)2 (X_c)1 + (X_0)1 (X_a)4 + (X_a)2 (X_b)1 (X_c)2 + (X_0)1 (X_c)4 + (X_a)2 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_a)2 (X_b)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)2 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-63
a 0 a a a
0 a a a 0
b 0 b b b
0 b b b 0
Codewords:
0 0 0 0 0
0 b b b 0
b 0 b b b
b b 0 0 b
0 a a a 0
0 c c c 0
b a c c b
b c a a b
a 0 a a a
a b c c a
c 0 c c c
c b a a c
a a 0 0 a
a c b b a
c a b b c
c c 0 0 c
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 6x3 + 3x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)2 (X_b)3 + (X_0)1 (X_b)4 + (X_0)2 (X_b)3 + (X_0)2 (X_a)3 + (X_0)2 (X_c)3 + (X_a)1 (X_b)2 (X_c)2 + (X_a)2 (X_b)2 (X_c)1 + (X_0)1 (X_a)4 + (X_a)2 (X_b)1 (X_c)2 + (X_0)1 (X_c)4 + (X_a)2 (X_b)1 (X_c)2 + (X_0)2 (X_a)3 + (X_a)2 (X_b)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)2 + (X_0)2 (X_c)3
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No
Generator Matrix-64
a 0 a a a
0 a a a a
b 0 b b b
0 b b b b
Codewords:
0 0 0 0 0
0 b b b b
b 0 b b b
b b 0 0 0
0 a a a a
0 c c c c
b a c c c
b c a a a
a 0 a a a
a b c c c
c 0 c c c
c b a a a
a a 0 0 0
a c b b b
c a b b b
c c 0 0 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3 + 6x4 + 6x5
Complete Weight Enumerator: (X_0)5 + (X_0)1 (X_b)4 + (X_0)1 (X_b)4 + (X_0)3 (X_b)2 + (X_0)1 (X_a)4 + (X_0)1 (X_c)4 + (X_a)1 (X_b)1 (X_c)3 + (X_a)3 (X_b)1 (X_c)1 + (X_0)1 (X_a)4 + (X_a)1 (X_b)1 (X_c)3 + (X_0)1 (X_c)4 + (X_a)3 (X_b)1 (X_c)1 + (X_0)3 (X_a)2 + (X_a)1 (X_b)3 (X_c)1 + (X_a)1 (X_b)3 (X_c)1 + (X_0)3 (X_c)2
Dual Codewords:
0 0 0 0 0
Is it a nice code?: No