n=3, k0=1, k1=1
Optimal Minimum Distance: 2
Generator Matrices that generate Codes having Optimal Minimum Distance: 4, 6,
Total No. of Codes having Optimal Minimum Distance: 2
Generator Matrices that generate Nice Codes : None
Total No. of Nice Codes: 0

Generator Matrix-1

a 0 0
b 0 0
0 c 0

Codewords:

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

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

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-2

a 0 0
b 0 0
0 c c

Codewords:

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

dmin: 1
Weight Enumerator: 1x0 + 3x1 + 1x2 + 3x3
Complete Weight Enumerator: (X_0)3 + (X_0)1 (X_c)2 + (X_0)2 (X_b)1 + (X_b)1 (X_c)2 + (X_0)2 (X_a)1 + (X_a)1 (X_c)2 + (X_0)2 (X_c)1 + (X_c)3

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-3

a 0 a
b 0 b
0 c 0

Codewords:

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

dmin: 1
Weight Enumerator: 1x0 + 1x1 + 3x2 + 3x3
Complete Weight Enumerator: (X_0)3 + (X_0)2 (X_c)1 + (X_0)1 (X_b)2 + (X_b)2 (X_c)1 + (X_0)1 (X_a)2 + (X_a)2 (X_c)1 + (X_0)1 (X_c)2 + (X_c)3

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-4

a 0 a
b 0 b
0 c c

Codewords:

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

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

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-5

a a 0
b b 0
0 c 0

Codewords:

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

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

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-6

a a 0
b b 0
0 c c

Codewords:

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

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

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-7

a a a
b b b
0 c 0

Codewords:

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

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

Dual Codewords:

0 0 0

Is it a nice code?: No

Generator Matrix-8

a a a
b b b
0 c c

Codewords:

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

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

Dual Codewords:

0 0 0

Is it a nice code?: No