n=4, k0=1, k1=1
Optimal Minimum Distance: 2
Generator Matrices that generate Codes having Optimal Minimum Distance: 6, 7, 8, 10, 11, 12, 14, 15, 16, 18, 19, 20, 23, 24, 26, 28, 30, 31,
Total No. of Codes having Optimal Minimum Distance: 18
Generator Matrices that generate Nice Codes : None
Total No. of Nice Codes: 0

Generator Matrix-1

a 0 0 0
b 0 0 0
0 c 0 0

Codewords:

0 0 0 0
0 c 0 0
b 0 0 0
b c 0 0
a 0 0 0
a c 0 0
c 0 0 0
c c 0 0

dmin: 1
Weight Enumerator: 1x0 + 4x1 + 3x2 + 0x3 + 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_a)1 + (X_0)2 (X_a)1 (X_c)1 + (X_0)3 (X_c)1 + (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
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?: No

Generator Matrix-2

a 0 0 0
b 0 0 0
0 c 0 c

Codewords:

0 0 0 0
0 c 0 c
b 0 0 0
b c 0 c
a 0 0 0
a c 0 c
c 0 0 0
c c 0 c

dmin: 1
Weight Enumerator: 1x0 + 3x1 + 1x2 + 3x3 + 0x4
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_a)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)3 (X_c)1 + (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
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?: No

Generator Matrix-3

a 0 0 0
b 0 0 0
0 c c 0

Codewords:

0 0 0 0
0 c c 0
b 0 0 0
b c c 0
a 0 0 0
a c c 0
c 0 0 0
c c c 0

dmin: 1
Weight Enumerator: 1x0 + 3x1 + 1x2 + 3x3 + 0x4
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_a)1 + (X_0)1 (X_a)1 (X_c)2 + (X_0)3 (X_c)1 + (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
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?: No

Generator Matrix-4

a 0 0 0
b 0 0 0
0 c c c

Codewords:

0 0 0 0
0 c c c
b 0 0 0
b c c c
a 0 0 0
a c c c
c 0 0 0
c c c c

dmin: 1
Weight Enumerator: 1x0 + 3x1 + 0x2 + 1x3 + 3x4
Complete Weight Enumerator: (X_0)4 + (X_0)1 (X_c)3 + (X_0)3 (X_b)1 + (X_b)1 (X_c)3 + (X_0)3 (X_a)1 + (X_a)1 (X_c)3 + (X_0)3 (X_c)1 + (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
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?: No

Generator Matrix-5

a 0 0 a
b 0 0 b
0 c 0 0

Codewords:

0 0 0 0
0 c 0 0
b 0 0 b
b c 0 b
a 0 0 a
a c 0 a
c 0 0 c
c c 0 c

dmin: 1
Weight Enumerator: 1x0 + 1x1 + 3x2 + 3x3 + 0x4
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_a)2 + (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 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-6

a 0 0 a
b 0 0 b
0 c 0 c

Codewords:

0 0 0 0
0 c 0 c
b 0 0 b
b c 0 a
a 0 0 a
a c 0 b
c 0 0 c
c c 0 0

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 5x2 + 2x3 + 0x4
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_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

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-7

a 0 0 a
b 0 0 b
0 c c 0

Codewords:

0 0 0 0
0 c c 0
b 0 0 b
b c c b
a 0 0 a
a c c a
c 0 0 c
c c c c

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 4x2 + 0x3 + 3x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)2 (X_b)2 + (X_b)2 (X_c)2 + (X_0)2 (X_a)2 + (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
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-8

a 0 0 a
b 0 0 b
0 c c c

Codewords:

0 0 0 0
0 c c c
b 0 0 b
b c c a
a 0 0 a
a c c b
c 0 0 c
c c c 0

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 2x3 + 2x4
Complete Weight Enumerator: (X_0)4 + (X_0)1 (X_c)3 + (X_0)2 (X_b)2 + (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)2 + (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
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-9

a 0 a 0
b 0 b 0
0 c 0 0

Codewords:

0 0 0 0
0 c 0 0
b 0 b 0
b c b 0
a 0 a 0
a c a 0
c 0 c 0
c c c 0

dmin: 1
Weight Enumerator: 1x0 + 1x1 + 3x2 + 3x3 + 0x4
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_a)2 + (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
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-10

a 0 a 0
b 0 b 0
0 c 0 c

Codewords:

0 0 0 0
0 c 0 c
b 0 b 0
b c b c
a 0 a 0
a c a c
c 0 c 0
c c c c

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 4x2 + 0x3 + 3x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)2 (X_b)2 + (X_b)2 (X_c)2 + (X_0)2 (X_a)2 + (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
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-11

a 0 a 0
b 0 b 0
0 c c 0

Codewords:

0 0 0 0
0 c c 0
b 0 b 0
b c a 0
a 0 a 0
a c b 0
c 0 c 0
c c 0 0

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 5x2 + 2x3 + 0x4
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_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

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-12

a 0 a 0
b 0 b 0
0 c c c

Codewords:

0 0 0 0
0 c c c
b 0 b 0
b c a c
a 0 a 0
a c b c
c 0 c 0
c c 0 c

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 2x3 + 2x4
Complete Weight Enumerator: (X_0)4 + (X_0)1 (X_c)3 + (X_0)2 (X_b)2 + (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)2 + (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 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-13

a 0 a a
b 0 b b
0 c 0 0

Codewords:

0 0 0 0
0 c 0 0
b 0 b b
b c b b
a 0 a a
a c a a
c 0 c c
c c c c

dmin: 1
Weight Enumerator: 1x0 + 1x1 + 0x2 + 3x3 + 3x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_0)1 (X_b)3 + (X_b)3 (X_c)1 + (X_0)1 (X_a)3 + (X_a)3 (X_c)1 + (X_0)1 (X_c)3 + (X_c)4

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-14

a 0 a a
b 0 b b
0 c 0 c

Codewords:

0 0 0 0
0 c 0 c
b 0 b b
b c b a
a 0 a a
a c a b
c 0 c c
c c c 0

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 1x2 + 4x3 + 2x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)1 (X_b)3 + (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_0)1 (X_c)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-15

a 0 a a
b 0 b b
0 c c 0

Codewords:

0 0 0 0
0 c c 0
b 0 b b
b c a b
a 0 a a
a c b a
c 0 c c
c c 0 c

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 1x2 + 4x3 + 2x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)1 (X_b)3 + (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_0)1 (X_c)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-16

a 0 a a
b 0 b b
0 c c c

Codewords:

0 0 0 0
0 c c c
b 0 b b
b c a a
a 0 a a
a c b b
c 0 c c
c c 0 0

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 1x2 + 4x3 + 2x4
Complete Weight Enumerator: (X_0)4 + (X_0)1 (X_c)3 + (X_0)1 (X_b)3 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)3 + (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
0 a 0 0
0 b 0 0
0 c 0 0

Is it a nice code?: No

Generator Matrix-17

a a 0 0
b b 0 0
0 c 0 0

Codewords:

0 0 0 0
0 c 0 0
b b 0 0
b a 0 0
a a 0 0
a b 0 0
c c 0 0
c 0 0 0

dmin: 1
Weight Enumerator: 1x0 + 2x1 + 5x2 + 0x3 + 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_a)2 + (X_0)2 (X_a)1 (X_b)1 + (X_0)2 (X_c)2 + (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

Is it a nice code?: No

Generator Matrix-18

a a 0 0
b b 0 0
0 c 0 c

Codewords:

0 0 0 0
0 c 0 c
b b 0 0
b a 0 c
a a 0 0
a b 0 c
c c 0 0
c 0 0 c

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 5x2 + 2x3 + 0x4
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_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

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-19

a a 0 0
b b 0 0
0 c c 0

Codewords:

0 0 0 0
0 c c 0
b b 0 0
b a c 0
a a 0 0
a b c 0
c c 0 0
c 0 c 0

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 5x2 + 2x3 + 0x4
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_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

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-20

a a 0 0
b b 0 0
0 c c c

Codewords:

0 0 0 0
0 c c c
b b 0 0
b a c c
a a 0 0
a b c c
c c 0 0
c 0 c c

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 2x3 + 2x4
Complete Weight Enumerator: (X_0)4 + (X_0)1 (X_c)3 + (X_0)2 (X_b)2 + (X_a)1 (X_b)1 (X_c)2 + (X_0)2 (X_a)2 + (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 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-21

a a 0 a
b b 0 b
0 c 0 0

Codewords:

0 0 0 0
0 c 0 0
b b 0 b
b a 0 b
a a 0 a
a b 0 a
c c 0 c
c 0 0 c

dmin: 1
Weight Enumerator: 1x0 + 1x1 + 1x2 + 5x3 + 0x4
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_a)3 + (X_0)1 (X_a)2 (X_b)1 + (X_0)1 (X_c)3 + (X_0)2 (X_c)2

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-22

a a 0 a
b b 0 b
0 c 0 c

Codewords:

0 0 0 0
0 c 0 c
b b 0 b
b a 0 a
a a 0 a
a b 0 b
c c 0 c
c 0 0 0

dmin: 1
Weight Enumerator: 1x0 + 1x1 + 1x2 + 5x3 + 0x4
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_a)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_c)3 + (X_0)3 (X_c)1

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-23

a a 0 a
b b 0 b
0 c c 0

Codewords:

0 0 0 0
0 c c 0
b b 0 b
b a c b
a a 0 a
a b c a
c c 0 c
c 0 c c

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 1x2 + 4x3 + 2x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)1 (X_b)3 + (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_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-24

a a 0 a
b b 0 b
0 c c c

Codewords:

0 0 0 0
0 c c c
b b 0 b
b a c a
a a 0 a
a b c b
c c 0 c
c 0 c 0

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 1x2 + 4x3 + 2x4
Complete Weight Enumerator: (X_0)4 + (X_0)1 (X_c)3 + (X_0)1 (X_b)3 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)3 + (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
0 0 a 0
0 0 b 0
0 0 c 0

Is it a nice code?: No

Generator Matrix-25

a a a 0
b b b 0
0 c 0 0

Codewords:

0 0 0 0
0 c 0 0
b b b 0
b a b 0
a a a 0
a b a 0
c c c 0
c 0 c 0

dmin: 1
Weight Enumerator: 1x0 + 1x1 + 1x2 + 5x3 + 0x4
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_a)3 + (X_0)1 (X_a)2 (X_b)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-26

a a a 0
b b b 0
0 c 0 c

Codewords:

0 0 0 0
0 c 0 c
b b b 0
b a b c
a a a 0
a b a c
c c c 0
c 0 c c

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 1x2 + 4x3 + 2x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_0)1 (X_b)3 + (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_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-27

a a a 0
b b b 0
0 c c 0

Codewords:

0 0 0 0
0 c c 0
b b b 0
b a a 0
a a a 0
a b b 0
c c c 0
c 0 0 0

dmin: 1
Weight Enumerator: 1x0 + 1x1 + 1x2 + 5x3 + 0x4
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_a)3 + (X_0)1 (X_a)1 (X_b)2 + (X_0)1 (X_c)3 + (X_0)3 (X_c)1

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-28

a a a 0
b b b 0
0 c c c

Codewords:

0 0 0 0
0 c c c
b b b 0
b a a c
a a a 0
a b b c
c c c 0
c 0 0 c

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 1x2 + 4x3 + 2x4
Complete Weight Enumerator: (X_0)4 + (X_0)1 (X_c)3 + (X_0)1 (X_b)3 + (X_a)2 (X_b)1 (X_c)1 + (X_0)1 (X_a)3 + (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
0 0 0 a
0 0 0 b
0 0 0 c

Is it a nice code?: No

Generator Matrix-29

a a a a
b b b b
0 c 0 0

Codewords:

0 0 0 0
0 c 0 0
b b b b
b a b b
a a a a
a b a a
c c c c
c 0 c c

dmin: 1
Weight Enumerator: 1x0 + 1x1 + 0x2 + 1x3 + 5x4
Complete Weight Enumerator: (X_0)4 + (X_0)3 (X_c)1 + (X_b)4 + (X_a)1 (X_b)3 + (X_a)4 + (X_a)3 (X_b)1 + (X_c)4 + (X_0)1 (X_c)3

Dual Codewords:

0 0 0 0

Is it a nice code?: No

Generator Matrix-30

a a a a
b b b b
0 c 0 c

Codewords:

0 0 0 0
0 c 0 c
b b b b
b a b a
a a a a
a b a b
c c c c
c 0 c 0

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 2x2 + 0x3 + 5x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_b)4 + (X_a)2 (X_b)2 + (X_a)4 + (X_a)2 (X_b)2 + (X_c)4 + (X_0)2 (X_c)2

Dual Codewords:

0 0 0 0

Is it a nice code?: No

Generator Matrix-31

a a a a
b b b b
0 c c 0

Codewords:

0 0 0 0
0 c c 0
b b b b
b a a b
a a a a
a b b a
c c c c
c 0 0 c

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 2x2 + 0x3 + 5x4
Complete Weight Enumerator: (X_0)4 + (X_0)2 (X_c)2 + (X_b)4 + (X_a)2 (X_b)2 + (X_a)4 + (X_a)2 (X_b)2 + (X_c)4 + (X_0)2 (X_c)2

Dual Codewords:

0 0 0 0

Is it a nice code?: No

Generator Matrix-32

a a a a
b b b b
0 c c c

Codewords:

0 0 0 0
0 c c c
b b b b
b a a a
a a a a
a b b b
c c c c
c 0 0 0

dmin: 1
Weight Enumerator: 1x0 + 1x1 + 0x2 + 1x3 + 5x4
Complete Weight Enumerator: (X_0)4 + (X_0)1 (X_c)3 + (X_b)4 + (X_a)3 (X_b)1 + (X_a)4 + (X_a)1 (X_b)3 + (X_c)4 + (X_0)3 (X_c)1

Dual Codewords:

0 0 0 0

Is it a nice code?: No