n=4, k0=1, k1=0
Optimal Minimum Distance: 4
Generator Matrices that generate Codes having Optimal Minimum Distance: 8,
Total No. of Codes having Optimal Minimum Distance: 1
Generator Matrices that generate Nice Codes : 1,
Total No. of Nice Codes: 1
Generator Matrix-1
a 0 0 0
b 0 0 0
Codewords:
0 0 0 0
b 0 0 0
a 0 0 0
c 0 0 0
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 0x2 + 0x3 + 0x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_b)1 + (X_0)3 (X_a)1 + (X_0)3 (X_c)1
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
0 a 0 0
0 a 0 a
0 a 0 b
0 a 0 c
0 a a 0
0 a a a
0 a a b
0 a a c
0 a b 0
0 a b a
0 a b b
0 a b c
0 a c 0
0 a c a
0 a c b
0 a c c
0 b 0 0
0 b 0 a
0 b 0 b
0 b 0 c
0 b a 0
0 b a a
0 b a b
0 b a c
0 b b 0
0 b b a
0 b b b
0 b b c
0 b c 0
0 b c a
0 b c b
0 b c c
0 c 0 0
0 c 0 a
0 c 0 b
0 c 0 c
0 c a 0
0 c a a
0 c a b
0 c a c
0 c b 0
0 c b a
0 c b b
0 c b c
0 c c 0
0 c c a
0 c c b
0 c c c
Is it a nice code?: Yes
Generator Matrix-2
a 0 0 a
b 0 0 b
Codewords:
0 0 0 0
b 0 0 b
a 0 0 a
c 0 0 c
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3 + 0x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_b)2 + (X_0)2 (X_a)2 + (X_0)2 (X_c)2
Dual Codewords:
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 0
Is it a nice code?: No
Generator Matrix-3
a 0 a 0
b 0 b 0
Codewords:
0 0 0 0
b 0 b 0
a 0 a 0
c 0 c 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3 + 0x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_b)2 + (X_0)2 (X_a)2 + (X_0)2 (X_c)2
Dual Codewords:
0 0 0 0
0 0 0 a
0 0 0 b
0 0 0 c
0 a 0 0
0 a 0 a
0 a 0 b
0 a 0 c
0 b 0 0
0 b 0 a
0 b 0 b
0 b 0 c
0 c 0 0
0 c 0 a
0 c 0 b
0 c 0 c
Is it a nice code?: No
Generator Matrix-4
a 0 a a
b 0 b b
Codewords:
0 0 0 0
b 0 b b
a 0 a a
c 0 c c
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 3x3 + 0x4
Complete Weight Enumerator: (X_0)4 + (X_0)1 (X_b)3 + (X_0)1 (X_a)3 + (X_0)1 (X_c)3
Dual Codewords:
0 0 0 0
0 a 0 0
0 b 0 0
0 c 0 0
Is it a nice code?: No
Generator Matrix-5
a a 0 0
b b 0 0
Codewords:
0 0 0 0
b b 0 0
a a 0 0
c c 0 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3 + 0x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_b)2 + (X_0)2 (X_a)2 + (X_0)2 (X_c)2
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-6
a a 0 a
b b 0 b
Codewords:
0 0 0 0
b b 0 b
a a 0 a
c c 0 c
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 3x3 + 0x4
Complete Weight Enumerator: (X_0)4 + (X_0)1 (X_b)3 + (X_0)1 (X_a)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 a a 0
b b b 0
Codewords:
0 0 0 0
b b b 0
a a a 0
c c c 0
dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 3x3 + 0x4
Complete Weight Enumerator: (X_0)4 + (X_0)1 (X_b)3 + (X_0)1 (X_a)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-8
a a a a
b b b b
Codewords:
0 0 0 0
b b b b
a a a a
c c c c
dmin: 4
Weight Enumerator: 1x0 + 0x1 + 0x2 + 0x3 + 3x4
Complete Weight Enumerator: (X_0)4 + (X_b)4 + (X_a)4 + (X_c)4
Dual Codewords:
0 0 0 0
Is it a nice code?: No