n=4, k0=2, k1=1
Optimal Minimum Distance: 2
Generator Matrices that generate Codes having Optimal Minimum Distance: 8, 14, 20, 26,
Total No. of Codes having Optimal Minimum Distance: 4
Generator Matrices that generate Nice Codes : None
Total No. of Nice Codes: 0
Generator Matrix-1
a 0 0 0
0 a 0 0
b 0 0 0
0 b 0 0
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b 0 0
0 b c 0
b 0 0 0
b 0 c 0
b b 0 0
b b c 0
0 a 0 0
0 a c 0
0 c 0 0
0 c c 0
b a 0 0
b a c 0
b c 0 0
b c c 0
a 0 0 0
a 0 c 0
a b 0 0
a b c 0
c 0 0 0
c 0 c 0
c b 0 0
c b c 0
a a 0 0
a a c 0
a c 0 0
a c c 0
c a 0 0
c a c 0
c c 0 0
c c c 0
dmin: 1
Weight Enumerator: 1x0 + 7x1 + 15x2 + 9x3 + 0x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)3 (X_b)1 + (X_0)2 (X_b)1 (X_c)1 + (X_0)3 (X_b)1 + (X_0)2 (X_b)1 (X_c)1 + (X_0)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)3 (X_a)1 + (X_0)2 (X_a)1 (X_c)1 + (X_0)3 (X_c)1 + (X_0)2 (X_c)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_b)1 (X_c)1 + (X_0)1 (X_b)1 (X_c)2 + (X_0)3 (X_a)1 + (X_0)2 (X_a)1 (X_c)1 + (X_0)2 (X_a)1 (X_b)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_c)1 + (X_0)2 (X_c)2 + (X_0)2 (X_b)1 (X_c)1 + (X_0)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)2 + (X_0)1 (X_a)2 (X_c)1 + (X_0)2 (X_a)1 (X_c)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)2 (X_a)1 (X_c)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)2 (X_c)2 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
0 0 0 a
0 0 0 b
0 0 0 c
0 0 a 0
0 0 a a
0 0 a b
0 0 a c
0 0 b 0
0 0 b a
0 0 b b
0 0 b c
0 0 c 0
0 0 c a
0 0 c b
0 0 c c
Is it a nice code?: No
Generator Matrix-2
a 0 0 0
0 a 0 0
b 0 0 0
0 b 0 0
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b 0 0
0 b c c
b 0 0 0
b 0 c c
b b 0 0
b b c c
0 a 0 0
0 a c c
0 c 0 0
0 c c c
b a 0 0
b a c c
b c 0 0
b c c c
a 0 0 0
a 0 c c
a b 0 0
a b c c
c 0 0 0
c 0 c c
c b 0 0
c b c c
a a 0 0
a a c c
a c 0 0
a c c c
c a 0 0
c a c c
c c 0 0
c c c c
dmin: 1
Weight Enumerator: 1x0 + 6x1 + 10x2 + 6x3 + 9x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)3 (X_b)1 + (X_0)1 (X_b)1 (X_c)2 + (X_0)3 (X_b)1 + (X_0)1 (X_b)1 (X_c)2 + (X_0)2 (X_b)2 + (X_b)2 (X_c)2 + (X_0)3 (X_a)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)3 (X_c)1 + (X_0)1 (X_c)3 + (X_0)2 (X_a)1 (X_b)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_b)1 (X_c)1 + (X_b)1 (X_c)3 + (X_0)3 (X_a)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)2 (X_a)1 (X_b)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)3 (X_c)1 + (X_0)1 (X_c)3 + (X_0)2 (X_b)1 (X_c)1 + (X_b)1 (X_c)3 + (X_0)2 (X_a)2 + (X_a)2 (X_c)2 + (X_0)2 (X_a)1 (X_c)1 + (X_a)1 (X_c)3 + (X_0)2 (X_a)1 (X_c)1 + (X_a)1 (X_c)3 + (X_0)2 (X_c)2 + (X_c)4
Dual Codewords:
0 0 0 0
0 0 0 a
0 0 0 b
0 0 0 c
0 0 a 0
0 0 a a
0 0 a b
0 0 a c
0 0 b 0
0 0 b a
0 0 b b
0 0 b c
0 0 c 0
0 0 c a
0 0 c b
0 0 c c
Is it a nice code?: No
Generator Matrix-3
a 0 0 0
0 a 0 a
b 0 0 0
0 b 0 b
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b 0 b
0 b c b
b 0 0 0
b 0 c 0
b b 0 b
b b c b
0 a 0 a
0 a c a
0 c 0 c
0 c c c
b a 0 a
b a c a
b c 0 c
b c c c
a 0 0 0
a 0 c 0
a b 0 b
a b c b
c 0 0 0
c 0 c 0
c b 0 b
c b c b
a a 0 a
a a c a
a c 0 c
a c c c
c a 0 a
c a c a
c c 0 c
c c c c
dmin: 1
Weight Enumerator: 1x0 + 4x1 + 6x2 + 12x3 + 9x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)3 (X_b)1 + (X_0)2 (X_b)1 (X_c)1 + (X_0)1 (X_b)3 + (X_b)3 (X_c)1 + (X_0)2 (X_a)2 + (X_0)1 (X_a)2 (X_c)1 + (X_0)2 (X_c)2 + (X_0)1 (X_c)3 + (X_0)1 (X_a)2 (X_b)1 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_b)1 (X_c)2 + (X_b)1 (X_c)3 + (X_0)3 (X_a)1 + (X_0)2 (X_a)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 + (X_a)1 (X_b)2 (X_c)1 + (X_0)3 (X_c)1 + (X_0)2 (X_c)2 + (X_0)1 (X_b)2 (X_c)1 + (X_b)2 (X_c)2 + (X_0)1 (X_a)3 + (X_a)3 (X_c)1 + (X_0)1 (X_a)1 (X_c)2 + (X_a)1 (X_c)3 + (X_0)1 (X_a)2 (X_c)1 + (X_a)2 (X_c)2 + (X_0)1 (X_c)3 + (X_c)4
Dual Codewords:
0 0 0 0
0 0 a 0
0 0 b 0
0 0 c 0
Is it a nice code?: No
Generator Matrix-4
a 0 0 0
0 a 0 a
b 0 0 0
0 b 0 b
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b 0 b
0 b c a
b 0 0 0
b 0 c c
b b 0 b
b b c a
0 a 0 a
0 a c b
0 c 0 c
0 c c 0
b a 0 a
b a c b
b c 0 c
b c c 0
a 0 0 0
a 0 c c
a b 0 b
a b c a
c 0 0 0
c 0 c c
c b 0 b
c b c a
a a 0 a
a a c b
a c 0 c
a c c 0
c a 0 a
c a c b
c c 0 c
c c c 0
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 5x2 + 17x3 + 6x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_b)1 + (X_0)1 (X_b)1 (X_c)2 + (X_0)1 (X_b)3 + (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_0)1 (X_a)2 (X_b)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_b)1 (X_c)2 + (X_0)1 (X_b)1 (X_c)2 + (X_0)3 (X_a)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 + (X_a)2 (X_b)1 (X_c)1 + (X_0)3 (X_c)1 + (X_0)1 (X_c)3 + (X_0)1 (X_b)2 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)3 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)1 (X_a)1 (X_c)2 + (X_0)1 (X_a)2 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_c)3 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
0 0 a 0
0 0 b 0
0 0 c 0
Is it a nice code?: No
Generator Matrix-5
a 0 0 a
0 a 0 0
b 0 0 b
0 b 0 0
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b 0 0
0 b c 0
b 0 0 b
b 0 c b
b b 0 b
b b c b
0 a 0 0
0 a c 0
0 c 0 0
0 c c 0
b a 0 b
b a c b
b c 0 b
b c c b
a 0 0 a
a 0 c a
a b 0 a
a b c a
c 0 0 c
c 0 c c
c b 0 c
c b c c
a a 0 a
a a c a
a c 0 a
a c c a
c a 0 c
c a c c
c c 0 c
c c c c
dmin: 1
Weight Enumerator: 1x0 + 4x1 + 6x2 + 12x3 + 9x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)3 (X_b)1 + (X_0)2 (X_b)1 (X_c)1 + (X_0)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)1 (X_b)3 + (X_b)3 (X_c)1 + (X_0)3 (X_a)1 + (X_0)2 (X_a)1 (X_c)1 + (X_0)3 (X_c)1 + (X_0)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_b)2 (X_c)1 + (X_b)2 (X_c)2 + (X_0)2 (X_a)2 + (X_0)1 (X_a)2 (X_c)1 + (X_0)1 (X_a)2 (X_b)1 + (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)2 + (X_0)1 (X_c)3 + (X_0)1 (X_b)1 (X_c)2 + (X_b)1 (X_c)3 + (X_0)1 (X_a)3 + (X_a)3 (X_c)1 + (X_0)1 (X_a)2 (X_c)1 + (X_a)2 (X_c)2 + (X_0)1 (X_a)1 (X_c)2 + (X_a)1 (X_c)3 + (X_0)1 (X_c)3 + (X_c)4
Dual Codewords:
0 0 0 0
0 0 a 0
0 0 b 0
0 0 c 0
Is it a nice code?: No
Generator Matrix-6
a 0 0 a
0 a 0 0
b 0 0 b
0 b 0 0
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b 0 0
0 b c c
b 0 0 b
b 0 c a
b b 0 b
b b c a
0 a 0 0
0 a c c
0 c 0 0
0 c c c
b a 0 b
b a c a
b c 0 b
b c c a
a 0 0 a
a 0 c b
a b 0 a
a b c b
c 0 0 c
c 0 c 0
c b 0 c
c b c 0
a a 0 a
a a c b
a c 0 a
a c c b
c a 0 c
c a c 0
c c 0 c
c c c 0
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 5x2 + 17x3 + 6x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)3 (X_b)1 + (X_0)1 (X_b)1 (X_c)2 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_b)3 + (X_a)1 (X_b)2 (X_c)1 + (X_0)3 (X_a)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)3 (X_c)1 + (X_0)1 (X_c)3 + (X_0)1 (X_a)1 (X_b)2 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_b)2 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)2 (X_b)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_0)1 (X_b)1 (X_c)2 + (X_0)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)3 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)2 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)1 (X_c)2 + (X_0)1 (X_a)1 (X_c)2 + (X_0)1 (X_c)3 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
0 0 a 0
0 0 b 0
0 0 c 0
Is it a nice code?: No
Generator Matrix-7
a 0 0 a
0 a 0 a
b 0 0 b
0 b 0 b
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b 0 b
0 b c b
b 0 0 b
b 0 c b
b b 0 0
b b c 0
0 a 0 a
0 a c a
0 c 0 c
0 c c c
b a 0 c
b a c c
b c 0 a
b c c a
a 0 0 a
a 0 c a
a b 0 c
a b c c
c 0 0 c
c 0 c c
c b 0 a
c b c a
a a 0 0
a a c 0
a c 0 b
a c c b
c a 0 b
c a c b
c c 0 0
c c c 0
dmin: 1
Weight Enumerator: 1x0 + 1x1 + 9x2 + 15x3 + 6x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)2 + (X_0)1 (X_a)2 (X_c)1 + (X_0)2 (X_c)2 + (X_0)1 (X_c)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)2 + (X_0)1 (X_a)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_c)2 + (X_0)1 (X_c)3 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)2 + (X_0)1 (X_a)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_c)2 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
0 0 a 0
0 0 b 0
0 0 c 0
Is it a nice code?: No
Generator Matrix-8
a 0 0 a
0 a 0 a
b 0 0 b
0 b 0 b
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b 0 b
0 b c a
b 0 0 b
b 0 c a
b b 0 0
b b c c
0 a 0 a
0 a c b
0 c 0 c
0 c c 0
b a 0 c
b a c 0
b c 0 a
b c c b
a 0 0 a
a 0 c b
a b 0 c
a b c 0
c 0 0 c
c 0 c 0
c b 0 a
c b c b
a a 0 0
a a c c
a c 0 b
a c c a
c a 0 b
c a c a
c c 0 0
c c c c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 12x2 + 12x3 + 7x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_b)2 + (X_b)2 (X_c)2 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_b)2 (X_c)2 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_b)2 (X_c)2 + (X_0)2 (X_a)2 + (X_a)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)2 (X_c)2 + (X_0)2 (X_c)2 + (X_c)4
Dual Codewords:
0 0 0 0
0 0 a 0
0 0 b 0
0 0 c 0
Is it a nice code?: No
Generator Matrix-9
a 0 0 0
0 a a 0
b 0 0 0
0 b b 0
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b b 0
0 b a 0
b 0 0 0
b 0 c 0
b b b 0
b b a 0
0 a a 0
0 a b 0
0 c c 0
0 c 0 0
b a a 0
b a b 0
b c c 0
b c 0 0
a 0 0 0
a 0 c 0
a b b 0
a b a 0
c 0 0 0
c 0 c 0
c b b 0
c b a 0
a a a 0
a a b 0
a c c 0
a c 0 0
c a a 0
c a b 0
c c c 0
c c 0 0
dmin: 1
Weight Enumerator: 1x0 + 5x1 + 11x2 + 15x3 + 0x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)2 (X_b)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)3 (X_b)1 + (X_0)2 (X_b)1 (X_c)1 + (X_0)1 (X_b)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)2 (X_a)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)2 (X_c)2 + (X_0)3 (X_c)1 + (X_0)1 (X_a)2 (X_b)1 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_b)1 (X_c)2 + (X_0)2 (X_b)1 (X_c)1 + (X_0)3 (X_a)1 + (X_0)2 (X_a)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_a)2 (X_b)1 + (X_0)3 (X_c)1 + (X_0)2 (X_c)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)2 (X_a)1 (X_c)1 + (X_0)1 (X_a)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_c)3 + (X_0)2 (X_c)2
Dual Codewords:
0 0 0 0
0 0 0 a
0 0 0 b
0 0 0 c
Is it a nice code?: No
Generator Matrix-10
a 0 0 0
0 a a 0
b 0 0 0
0 b b 0
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b b 0
0 b a c
b 0 0 0
b 0 c c
b b b 0
b b a c
0 a a 0
0 a b c
0 c c 0
0 c 0 c
b a a 0
b a b c
b c c 0
b c 0 c
a 0 0 0
a 0 c c
a b b 0
a b a c
c 0 0 0
c 0 c c
c b b 0
c b a c
a a a 0
a a b c
a c c 0
a c 0 c
c a a 0
c a b c
c c c 0
c c 0 c
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 5x2 + 17x3 + 6x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)3 (X_b)1 + (X_0)1 (X_b)1 (X_c)2 + (X_0)1 (X_b)3 + (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_0)1 (X_a)2 (X_b)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_b)1 (X_c)2 + (X_0)1 (X_b)1 (X_c)2 + (X_0)3 (X_a)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 + (X_a)2 (X_b)1 (X_c)1 + (X_0)3 (X_c)1 + (X_0)1 (X_c)3 + (X_0)1 (X_b)2 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)3 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)1 (X_a)1 (X_c)2 + (X_0)1 (X_a)2 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_c)3 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
0 0 0 a
0 0 0 b
0 0 0 c
Is it a nice code?: No
Generator Matrix-11
a 0 0 0
0 a a a
b 0 0 0
0 b b b
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b b b
0 b a b
b 0 0 0
b 0 c 0
b b b b
b b a b
0 a a a
0 a b a
0 c c c
0 c 0 c
b a a a
b a b a
b c c c
b c 0 c
a 0 0 0
a 0 c 0
a b b b
a b a b
c 0 0 0
c 0 c 0
c b b b
c b a b
a a a a
a a b a
a c c c
a c 0 c
c a a a
c a b a
c c c c
c c 0 c
dmin: 1
Weight Enumerator: 1x0 + 4x1 + 4x2 + 8x3 + 15x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)1 (X_b)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)3 (X_b)1 + (X_0)2 (X_b)1 (X_c)1 + (X_b)4 + (X_a)1 (X_b)3 + (X_0)1 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 + (X_0)1 (X_c)3 + (X_0)2 (X_c)2 + (X_a)3 (X_b)1 + (X_a)2 (X_b)2 + (X_b)1 (X_c)3 + (X_0)1 (X_b)1 (X_c)2 + (X_0)3 (X_a)1 + (X_0)2 (X_a)1 (X_c)1 + (X_a)1 (X_b)3 + (X_a)2 (X_b)2 + (X_0)3 (X_c)1 + (X_0)2 (X_c)2 + (X_b)3 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_a)4 + (X_a)3 (X_b)1 + (X_a)1 (X_c)3 + (X_0)1 (X_a)1 (X_c)2 + (X_a)3 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_c)4 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-12
a 0 0 0
0 a a a
b 0 0 0
0 b b b
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b b b
0 b a a
b 0 0 0
b 0 c c
b b b b
b b a a
0 a a a
0 a b b
0 c c c
0 c 0 0
b a a a
b a b b
b c c c
b c 0 0
a 0 0 0
a 0 c c
a b b b
a b a a
c 0 0 0
c 0 c c
c b b b
c b a a
a a a a
a a b b
a c c c
a c 0 0
c a a a
c a b b
c c c c
c c 0 0
dmin: 1
Weight Enumerator: 1x0 + 4x1 + 4x2 + 8x3 + 15x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)1 (X_b)3 + (X_0)1 (X_a)2 (X_b)1 + (X_0)3 (X_b)1 + (X_0)1 (X_b)1 (X_c)2 + (X_b)4 + (X_a)2 (X_b)2 + (X_0)1 (X_a)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_c)3 + (X_0)3 (X_c)1 + (X_a)3 (X_b)1 + (X_a)1 (X_b)3 + (X_b)1 (X_c)3 + (X_0)2 (X_b)1 (X_c)1 + (X_0)3 (X_a)1 + (X_0)1 (X_a)1 (X_c)2 + (X_a)1 (X_b)3 + (X_a)3 (X_b)1 + (X_0)3 (X_c)1 + (X_0)1 (X_c)3 + (X_b)3 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)4 + (X_a)2 (X_b)2 + (X_a)1 (X_c)3 + (X_0)2 (X_a)1 (X_c)1 + (X_a)3 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_c)4 + (X_0)2 (X_c)2
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-13
a 0 0 a
0 a a 0
b 0 0 b
0 b b 0
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b b 0
0 b a 0
b 0 0 b
b 0 c b
b b b b
b b a b
0 a a 0
0 a b 0
0 c c 0
0 c 0 0
b a a b
b a b b
b c c b
b c 0 b
a 0 0 a
a 0 c a
a b b a
a b a a
c 0 0 c
c 0 c c
c b b c
c b a c
a a a a
a a b a
a c c a
a c 0 a
c a a c
c a b c
c c c c
c c 0 c
dmin: 1
Weight Enumerator: 1x0 + 2x1 + 8x2 + 6x3 + 15x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)2 (X_b)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)1 + (X_b)4 + (X_a)1 (X_b)3 + (X_0)2 (X_a)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)2 (X_c)2 + (X_0)3 (X_c)1 + (X_a)2 (X_b)2 + (X_a)1 (X_b)3 + (X_b)2 (X_c)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)2 + (X_0)1 (X_a)2 (X_c)1 + (X_a)2 (X_b)2 + (X_a)3 (X_b)1 + (X_0)2 (X_c)2 + (X_0)1 (X_c)3 + (X_b)2 (X_c)2 + (X_a)1 (X_b)1 (X_c)2 + (X_a)4 + (X_a)3 (X_b)1 + (X_a)2 (X_c)2 + (X_0)1 (X_a)2 (X_c)1 + (X_a)2 (X_c)2 + (X_a)1 (X_b)1 (X_c)2 + (X_c)4 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-14
a 0 0 a
0 a a 0
b 0 0 b
0 b b 0
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b b 0
0 b a c
b 0 0 b
b 0 c a
b b b b
b b a a
0 a a 0
0 a b c
0 c c 0
0 c 0 c
b a a b
b a b a
b c c b
b c 0 a
a 0 0 a
a 0 c b
a b b a
a b a b
c 0 0 c
c 0 c 0
c b b c
c b a 0
a a a a
a a b b
a c c a
a c 0 b
c a a c
c a b 0
c c c c
c c 0 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 10x2 + 8x3 + 13x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_b)4 + (X_a)2 (X_b)2 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_a)2 (X_b)2 + (X_a)2 (X_b)2 + (X_b)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)2 (X_b)2 + (X_a)2 (X_b)2 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_b)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)4 + (X_a)2 (X_b)2 + (X_a)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_c)4 + (X_0)2 (X_c)2
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-15
a 0 0 a
0 a a a
b 0 0 b
0 b b b
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b b b
0 b a b
b 0 0 b
b 0 c b
b b b 0
b b a 0
0 a a a
0 a b a
0 c c c
0 c 0 c
b a a c
b a b c
b c c a
b c 0 a
a 0 0 a
a 0 c a
a b b c
a b a c
c 0 0 c
c 0 c c
c b b a
c b a a
a a a 0
a a b 0
a c c b
a c 0 b
c a a b
c a b b
c c c 0
c c 0 0
dmin: 1
Weight Enumerator: 1x0 + 1x1 + 5x2 + 15x3 + 10x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)1 (X_b)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)1 (X_b)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 + (X_0)1 (X_c)3 + (X_0)2 (X_c)2 + (X_a)2 (X_b)1 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_a)2 + (X_0)1 (X_a)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)2 + (X_0)1 (X_c)3 + (X_a)1 (X_b)2 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_c)3 + (X_0)2 (X_c)2
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-16
a 0 0 a
0 a a a
b 0 0 b
0 b b b
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b b b
0 b a a
b 0 0 b
b 0 c a
b b b 0
b b a c
0 a a a
0 a b b
0 c c c
0 c 0 0
b a a c
b a b 0
b c c a
b c 0 b
a 0 0 a
a 0 c b
a b b c
a b a 0
c 0 0 c
c 0 c 0
c b b a
c b a b
a a a 0
a a b c
a c c b
a c 0 a
c a a b
c a b a
c c c 0
c c 0 c
dmin: 1
Weight Enumerator: 1x0 + 1x1 + 5x2 + 15x3 + 10x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)1 (X_b)3 + (X_0)1 (X_a)2 (X_b)1 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_b)3 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_c)3 + (X_0)3 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)2 (X_b)1 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_a)1 (X_b)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)3 + (X_a)2 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)2 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_c)3 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-17
a 0 a 0
0 a 0 0
b 0 b 0
0 b 0 0
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b 0 0
0 b c 0
b 0 b 0
b 0 a 0
b b b 0
b b a 0
0 a 0 0
0 a c 0
0 c 0 0
0 c c 0
b a b 0
b a a 0
b c b 0
b c a 0
a 0 a 0
a 0 b 0
a b a 0
a b b 0
c 0 c 0
c 0 0 0
c b c 0
c b 0 0
a a a 0
a a b 0
a c a 0
a c b 0
c a c 0
c a 0 0
c c c 0
c c 0 0
dmin: 1
Weight Enumerator: 1x0 + 5x1 + 11x2 + 15x3 + 0x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)3 (X_b)1 + (X_0)2 (X_b)1 (X_c)1 + (X_0)2 (X_b)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)1 (X_b)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)3 (X_a)1 + (X_0)2 (X_a)1 (X_c)1 + (X_0)3 (X_c)1 + (X_0)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_a)2 (X_b)1 + (X_0)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_a)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)1 (X_a)2 (X_b)1 + (X_0)1 (X_a)1 (X_b)2 + (X_0)2 (X_c)2 + (X_0)3 (X_c)1 + (X_0)1 (X_b)1 (X_c)2 + (X_0)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 + (X_0)1 (X_a)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)2 (X_a)1 (X_c)1 + (X_0)1 (X_c)3 + (X_0)2 (X_c)2
Dual Codewords:
0 0 0 0
0 0 0 a
0 0 0 b
0 0 0 c
Is it a nice code?: No
Generator Matrix-18
a 0 a 0
0 a 0 0
b 0 b 0
0 b 0 0
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b 0 0
0 b c c
b 0 b 0
b 0 a c
b b b 0
b b a c
0 a 0 0
0 a c c
0 c 0 0
0 c c c
b a b 0
b a a c
b c b 0
b c a c
a 0 a 0
a 0 b c
a b a 0
a b b c
c 0 c 0
c 0 0 c
c b c 0
c b 0 c
a a a 0
a a b c
a c a 0
a c b c
c a c 0
c a 0 c
c c c 0
c c 0 c
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 5x2 + 17x3 + 6x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)3 (X_b)1 + (X_0)1 (X_b)1 (X_c)2 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_b)3 + (X_a)1 (X_b)2 (X_c)1 + (X_0)3 (X_a)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)3 (X_c)1 + (X_0)1 (X_c)3 + (X_0)1 (X_a)1 (X_b)2 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_b)2 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)2 (X_b)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_0)1 (X_b)1 (X_c)2 + (X_0)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)3 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)2 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)1 (X_c)2 + (X_0)1 (X_a)1 (X_c)2 + (X_0)1 (X_c)3 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
0 0 0 a
0 0 0 b
0 0 0 c
Is it a nice code?: No
Generator Matrix-19
a 0 a 0
0 a 0 a
b 0 b 0
0 b 0 b
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b 0 b
0 b c b
b 0 b 0
b 0 a 0
b b b b
b b a b
0 a 0 a
0 a c a
0 c 0 c
0 c c c
b a b a
b a a a
b c b c
b c a c
a 0 a 0
a 0 b 0
a b a b
a b b b
c 0 c 0
c 0 0 0
c b c b
c b 0 b
a a a a
a a b a
a c a c
a c b c
c a c a
c a 0 a
c c c c
c c 0 c
dmin: 1
Weight Enumerator: 1x0 + 2x1 + 8x2 + 6x3 + 15x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)2 (X_b)2 + (X_0)2 (X_a)1 (X_b)1 + (X_b)4 + (X_a)1 (X_b)3 + (X_0)2 (X_a)2 + (X_0)1 (X_a)2 (X_c)1 + (X_0)2 (X_c)2 + (X_0)1 (X_c)3 + (X_a)2 (X_b)2 + (X_a)3 (X_b)1 + (X_b)2 (X_c)2 + (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)2 + (X_0)2 (X_a)1 (X_b)1 + (X_a)2 (X_b)2 + (X_a)1 (X_b)3 + (X_0)2 (X_c)2 + (X_0)3 (X_c)1 + (X_b)2 (X_c)2 + (X_0)1 (X_b)2 (X_c)1 + (X_a)4 + (X_a)3 (X_b)1 + (X_a)2 (X_c)2 + (X_a)1 (X_b)1 (X_c)2 + (X_a)2 (X_c)2 + (X_0)1 (X_a)2 (X_c)1 + (X_c)4 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-20
a 0 a 0
0 a 0 a
b 0 b 0
0 b 0 b
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b 0 b
0 b c a
b 0 b 0
b 0 a c
b b b b
b b a a
0 a 0 a
0 a c b
0 c 0 c
0 c c 0
b a b a
b a a b
b c b c
b c a 0
a 0 a 0
a 0 b c
a b a b
a b b a
c 0 c 0
c 0 0 c
c b c b
c b 0 a
a a a a
a a b b
a c a c
a c b 0
c a c a
c a 0 b
c c c c
c c 0 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 10x2 + 8x3 + 13x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_b)4 + (X_a)2 (X_b)2 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_a)2 (X_b)2 + (X_a)2 (X_b)2 + (X_b)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)2 (X_b)2 + (X_a)2 (X_b)2 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_b)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)4 + (X_a)2 (X_b)2 + (X_a)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_c)4 + (X_0)2 (X_c)2
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-21
a 0 a a
0 a 0 0
b 0 b b
0 b 0 0
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b 0 0
0 b c 0
b 0 b b
b 0 a b
b b b b
b b a b
0 a 0 0
0 a c 0
0 c 0 0
0 c c 0
b a b b
b a a b
b c b b
b c a b
a 0 a a
a 0 b a
a b a a
a b b a
c 0 c c
c 0 0 c
c b c c
c b 0 c
a a a a
a a b a
a c a a
a c b a
c a c c
c a 0 c
c c c c
c c 0 c
dmin: 1
Weight Enumerator: 1x0 + 4x1 + 4x2 + 8x3 + 15x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)3 (X_b)1 + (X_0)2 (X_b)1 (X_c)1 + (X_0)1 (X_b)3 + (X_0)1 (X_a)1 (X_b)2 + (X_b)4 + (X_a)1 (X_b)3 + (X_0)3 (X_a)1 + (X_0)2 (X_a)1 (X_c)1 + (X_0)3 (X_c)1 + (X_0)2 (X_c)2 + (X_a)1 (X_b)3 + (X_a)2 (X_b)2 + (X_b)3 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 + (X_a)3 (X_b)1 + (X_a)2 (X_b)2 + (X_0)1 (X_c)3 + (X_0)2 (X_c)2 + (X_b)1 (X_c)3 + (X_0)1 (X_b)1 (X_c)2 + (X_a)4 + (X_a)3 (X_b)1 + (X_a)3 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)1 (X_c)3 + (X_0)1 (X_a)1 (X_c)2 + (X_c)4 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-22
a 0 a a
0 a 0 0
b 0 b b
0 b 0 0
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b 0 0
0 b c c
b 0 b b
b 0 a a
b b b b
b b a a
0 a 0 0
0 a c c
0 c 0 0
0 c c c
b a b b
b a a a
b c b b
b c a a
a 0 a a
a 0 b b
a b a a
a b b b
c 0 c c
c 0 0 0
c b c c
c b 0 0
a a a a
a a b b
a c a a
a c b b
c a c c
c a 0 0
c c c c
c c 0 0
dmin: 1
Weight Enumerator: 1x0 + 4x1 + 4x2 + 8x3 + 15x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)3 (X_b)1 + (X_0)1 (X_b)1 (X_c)2 + (X_0)1 (X_b)3 + (X_0)1 (X_a)2 (X_b)1 + (X_b)4 + (X_a)2 (X_b)2 + (X_0)3 (X_a)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)3 (X_c)1 + (X_0)1 (X_c)3 + (X_a)1 (X_b)3 + (X_a)3 (X_b)1 + (X_b)3 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)1 (X_b)2 + (X_a)3 (X_b)1 + (X_a)1 (X_b)3 + (X_0)1 (X_c)3 + (X_0)3 (X_c)1 + (X_b)1 (X_c)3 + (X_0)2 (X_b)1 (X_c)1 + (X_a)4 + (X_a)2 (X_b)2 + (X_a)3 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_a)1 (X_c)3 + (X_0)2 (X_a)1 (X_c)1 + (X_c)4 + (X_0)2 (X_c)2
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-23
a 0 a a
0 a 0 a
b 0 b b
0 b 0 b
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b 0 b
0 b c b
b 0 b b
b 0 a b
b b b 0
b b a 0
0 a 0 a
0 a c a
0 c 0 c
0 c c c
b a b c
b a a c
b c b a
b c a a
a 0 a a
a 0 b a
a b a c
a b b c
c 0 c c
c 0 0 c
c b c a
c b 0 a
a a a 0
a a b 0
a c a b
a c b b
c a c b
c a 0 b
c c c 0
c c 0 0
dmin: 1
Weight Enumerator: 1x0 + 1x1 + 5x2 + 15x3 + 10x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)1 (X_b)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_b)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)2 (X_a)2 + (X_0)1 (X_a)2 (X_c)1 + (X_0)2 (X_c)2 + (X_0)1 (X_c)3 + (X_a)1 (X_b)2 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_c)3 + (X_0)2 (X_c)2 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_c)3 + (X_0)2 (X_c)2
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-24
a 0 a a
0 a 0 a
b 0 b b
0 b 0 b
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b 0 b
0 b c a
b 0 b b
b 0 a a
b b b 0
b b a c
0 a 0 a
0 a c b
0 c 0 c
0 c c 0
b a b c
b a a 0
b c b a
b c a b
a 0 a a
a 0 b b
a b a c
a b b 0
c 0 c c
c 0 0 0
c b c a
c b 0 b
a a a 0
a a b c
a c a b
a c b a
c a c b
c a 0 a
c c c 0
c c 0 c
dmin: 1
Weight Enumerator: 1x0 + 1x1 + 5x2 + 15x3 + 10x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_b)3 + (X_0)1 (X_a)2 (X_b)1 + (X_0)1 (X_b)3 + (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)2 (X_b)1 + (X_a)1 (X_b)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)1 (X_b)2 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_c)3 + (X_0)3 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)3 + (X_a)2 (X_b)1 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)2 (X_c)1 + (X_0)1 (X_c)3 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-25
a 0 a 0
0 a a 0
b 0 b 0
0 b b 0
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b b 0
0 b a 0
b 0 b 0
b 0 a 0
b b 0 0
b b c 0
0 a a 0
0 a b 0
0 c c 0
0 c 0 0
b a c 0
b a 0 0
b c a 0
b c b 0
a 0 a 0
a 0 b 0
a b c 0
a b 0 0
c 0 c 0
c 0 0 0
c b a 0
c b b 0
a a 0 0
a a c 0
a c b 0
a c a 0
c a b 0
c a a 0
c c 0 0
c c c 0
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 15x2 + 13x3 + 0x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)2 (X_b)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)2 (X_b)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)2 (X_c)2 + (X_0)3 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_a)1 (X_b)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_a)1 (X_b)1 + (X_0)2 (X_c)2 + (X_0)3 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)2 + (X_0)1 (X_a)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)2 (X_c)1 + (X_0)2 (X_c)2 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
0 0 0 a
0 0 0 b
0 0 0 c
Is it a nice code?: No
Generator Matrix-26
a 0 a 0
0 a a 0
b 0 b 0
0 b b 0
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b b 0
0 b a c
b 0 b 0
b 0 a c
b b 0 0
b b c c
0 a a 0
0 a b c
0 c c 0
0 c 0 c
b a c 0
b a 0 c
b c a 0
b c b c
a 0 a 0
a 0 b c
a b c 0
a b 0 c
c 0 c 0
c 0 0 c
c b a 0
c b b c
a a 0 0
a a c c
a c b 0
a c a c
c a b 0
c a a c
c c 0 0
c c c c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 12x2 + 12x3 + 7x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_b)2 + (X_b)2 (X_c)2 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_b)2 (X_c)2 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_b)2 (X_c)2 + (X_0)2 (X_a)2 + (X_a)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)2 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)2 (X_c)2 + (X_0)2 (X_c)2 + (X_c)4
Dual Codewords:
0 0 0 0
0 0 0 a
0 0 0 b
0 0 0 c
Is it a nice code?: No
Generator Matrix-27
a 0 a 0
0 a a a
b 0 b 0
0 b b b
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b b b
0 b a b
b 0 b 0
b 0 a 0
b b 0 b
b b c b
0 a a a
0 a b a
0 c c c
0 c 0 c
b a c a
b a 0 a
b c a c
b c b c
a 0 a 0
a 0 b 0
a b c b
a b 0 b
c 0 c 0
c 0 0 0
c b a b
c b b b
a a 0 a
a a c a
a c b c
a c a c
c a b a
c a a a
c c 0 c
c c c c
dmin: 1
Weight Enumerator: 1x0 + 2x1 + 6x2 + 10x3 + 13x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)1 (X_b)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)2 (X_b)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)1 (X_b)3 + (X_b)3 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 + (X_0)1 (X_c)3 + (X_0)2 (X_c)2 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)2 (X_b)1 + (X_a)1 (X_b)1 (X_c)2 + (X_b)2 (X_c)2 + (X_0)2 (X_a)2 + (X_0)2 (X_a)1 (X_b)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 + (X_0)2 (X_c)2 + (X_0)3 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_b)3 (X_c)1 + (X_0)1 (X_a)3 + (X_a)3 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_a)2 (X_c)2 + (X_a)2 (X_b)1 (X_c)1 + (X_a)3 (X_c)1 + (X_0)1 (X_c)3 + (X_c)4
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-28
a 0 a 0
0 a a a
b 0 b 0
0 b b b
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b b b
0 b a a
b 0 b 0
b 0 a c
b b 0 b
b b c a
0 a a a
0 a b b
0 c c c
0 c 0 0
b a c a
b a 0 b
b c a c
b c b 0
a 0 a 0
a 0 b c
a b c b
a b 0 a
c 0 c 0
c 0 0 c
c b a b
c b b a
a a 0 a
a a c b
a c b c
a c a 0
c a b a
c a a b
c c 0 c
c c c 0
dmin: 1
Weight Enumerator: 1x0 + 1x1 + 5x2 + 15x3 + 10x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)1 (X_b)3 + (X_0)1 (X_a)2 (X_b)1 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_b)3 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_c)3 + (X_0)3 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)2 (X_b)1 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_a)1 (X_b)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)3 + (X_a)2 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)2 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_c)3 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-29
a 0 a a
0 a a 0
b 0 b b
0 b b 0
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b b 0
0 b a 0
b 0 b b
b 0 a b
b b 0 b
b b c b
0 a a 0
0 a b 0
0 c c 0
0 c 0 0
b a c b
b a 0 b
b c a b
b c b b
a 0 a a
a 0 b a
a b c a
a b 0 a
c 0 c c
c 0 0 c
c b a c
c b b c
a a 0 a
a a c a
a c b a
a c a a
c a b c
c a a c
c c 0 c
c c c c
dmin: 1
Weight Enumerator: 1x0 + 2x1 + 6x2 + 10x3 + 13x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)2 (X_b)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)1 (X_b)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_b)3 + (X_b)3 (X_c)1 + (X_0)2 (X_a)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)2 (X_c)2 + (X_0)3 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 + (X_a)1 (X_b)2 (X_c)1 + (X_b)3 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)2 (X_b)1 + (X_0)1 (X_c)3 + (X_0)2 (X_c)2 + (X_a)1 (X_b)1 (X_c)2 + (X_b)2 (X_c)2 + (X_0)1 (X_a)3 + (X_a)3 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)3 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_a)2 (X_c)2 + (X_0)1 (X_c)3 + (X_c)4
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-30
a 0 a a
0 a a 0
b 0 b b
0 b b 0
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b b 0
0 b a c
b 0 b b
b 0 a a
b b 0 b
b b c a
0 a a 0
0 a b c
0 c c 0
0 c 0 c
b a c b
b a 0 a
b c a b
b c b a
a 0 a a
a 0 b b
a b c a
a b 0 b
c 0 c c
c 0 0 0
c b a c
c b b 0
a a 0 a
a a c b
a c b a
a c a b
c a b c
c a a 0
c c 0 c
c c c 0
dmin: 1
Weight Enumerator: 1x0 + 1x1 + 5x2 + 15x3 + 10x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)2 (X_b)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_b)3 + (X_0)1 (X_a)2 (X_b)1 + (X_0)1 (X_b)3 + (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)2 (X_c)2 + (X_0)2 (X_c)2 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)2 (X_b)1 + (X_a)1 (X_b)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)1 (X_b)2 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_c)3 + (X_0)3 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)3 + (X_a)2 (X_b)1 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)2 (X_c)1 + (X_0)1 (X_c)3 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-31
a 0 a a
0 a a a
b 0 b b
0 b b b
0 0 c 0
Codewords:
0 0 0 0
0 0 c 0
0 b b b
0 b a b
b 0 b b
b 0 a b
b b 0 0
b b c 0
0 a a a
0 a b a
0 c c c
0 c 0 c
b a c c
b a 0 c
b c a a
b c b a
a 0 a a
a 0 b a
a b c c
a b 0 c
c 0 c c
c 0 0 c
c b a a
c b b a
a a 0 0
a a c 0
a c b b
a c a b
c a b b
c a a b
c c 0 0
c c c 0
dmin: 1
Weight Enumerator: 1x0 + 1x1 + 5x2 + 15x3 + 10x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)1 (X_b)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_b)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)2 (X_b)2 + (X_0)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 + (X_0)1 (X_c)3 + (X_0)2 (X_c)2 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)2 (X_b)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)1 (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_c)3 + (X_0)2 (X_c)2 + (X_a)2 (X_b)1 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_0)2 (X_a)2 + (X_0)1 (X_a)2 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_0)2 (X_c)2 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
Is it a nice code?: No
Generator Matrix-32
a 0 a a
0 a a a
b 0 b b
0 b b b
0 0 c c
Codewords:
0 0 0 0
0 0 c c
0 b b b
0 b a a
b 0 b b
b 0 a a
b b 0 0
b b c c
0 a a a
0 a b b
0 c c c
0 c 0 0
b a c c
b a 0 0
b c a a
b c b b
a 0 a a
a 0 b b
a b c c
a b 0 0
c 0 c c
c 0 0 0
c b a a
c b b b
a a 0 0
a a c c
a c b b
a c a a
c a b b
c a a a
c c 0 0
c c c c
dmin: 1
Weight Enumerator: 1x0 + 2x1 + 6x2 + 10x3 + 13x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)1 (X_b)3 + (X_0)1 (X_a)2 (X_b)1 + (X_0)1 (X_b)3 + (X_0)1 (X_a)2 (X_b)1 + (X_0)2 (X_b)2 + (X_b)2 (X_c)2 + (X_0)1 (X_a)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_c)3 + (X_0)3 (X_c)1 + (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)1 (X_b)1 + (X_a)2 (X_b)1 (X_c)1 + (X_b)3 (X_c)1 + (X_0)1 (X_a)3 + (X_0)1 (X_a)1 (X_b)2 + (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)1 (X_c)3 + (X_0)3 (X_c)1 + (X_a)2 (X_b)1 (X_c)1 + (X_b)3 (X_c)1 + (X_0)2 (X_a)2 + (X_a)2 (X_c)2 + (X_a)1 (X_b)2 (X_c)1 + (X_a)3 (X_c)1 + (X_a)1 (X_b)2 (X_c)1 + (X_a)3 (X_c)1 + (X_0)2 (X_c)2 + (X_c)4
Dual Codewords:
0 0 0 0
Is it a nice code?: No