n=6, k0=1, k1=0
Optimal Minimum Distance: 6
Generator Matrices that generate Codes having Optimal Minimum Distance: 32,
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 0 0
b 0 0 0 0 0

Codewords:

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

dmin: 1
Weight Enumerator: 1x⁰ + 3x¹ + 0x² + 0x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)⁵ (X_b)¹ + (X_0)⁵ (X_a)¹ + (X_0)⁵ (X_c)¹

Dual Codewords:

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

Is it a nice code?: Yes

Generator Matrix-2

a 0 0 0 0 a
b 0 0 0 0 b

Codewords:

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

dmin: 2
Weight Enumerator: 1x⁰ + 0x¹ + 3x² + 0x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)⁴ (X_b)² + (X_0)⁴ (X_a)² + (X_0)⁴ (X_c)²

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-3

a 0 0 0 a 0
b 0 0 0 b 0

Codewords:

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

dmin: 2
Weight Enumerator: 1x⁰ + 0x¹ + 3x² + 0x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)⁴ (X_b)² + (X_0)⁴ (X_a)² + (X_0)⁴ (X_c)²

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-4

a 0 0 0 a a
b 0 0 0 b b

Codewords:

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

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-5

a 0 0 a 0 0
b 0 0 b 0 0

Codewords:

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

dmin: 2
Weight Enumerator: 1x⁰ + 0x¹ + 3x² + 0x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)⁴ (X_b)² + (X_0)⁴ (X_a)² + (X_0)⁴ (X_c)²

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-6

a 0 0 a 0 a
b 0 0 b 0 b

Codewords:

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

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-7

a 0 0 a a 0
b 0 0 b b 0

Codewords:

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

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-8

a 0 0 a a a
b 0 0 b b b

Codewords:

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

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-9

a 0 a 0 0 0
b 0 b 0 0 0

Codewords:

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

dmin: 2
Weight Enumerator: 1x⁰ + 0x¹ + 3x² + 0x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)⁴ (X_b)² + (X_0)⁴ (X_a)² + (X_0)⁴ (X_c)²

Dual Codewords:

Is it a nice code?: No

Generator Matrix-10

a 0 a 0 0 a
b 0 b 0 0 b

Codewords:

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

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-11

a 0 a 0 a 0
b 0 b 0 b 0

Codewords:

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

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-12

a 0 a 0 a a
b 0 b 0 b b

Codewords:

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

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-13

a 0 a a 0 0
b 0 b b 0 0

Codewords:

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

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-14

a 0 a a 0 a
b 0 b b 0 b

Codewords:

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

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-15

a 0 a a a 0
b 0 b b b 0

Codewords:

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

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-16

a 0 a a a a
b 0 b b b b

Codewords:

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

dmin: 5
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 0x⁴ + 3x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)¹ (X_b)⁵ + (X_0)¹ (X_a)⁵ + (X_0)¹ (X_c)⁵

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-17

a a 0 0 0 0
b b 0 0 0 0

Codewords:

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

dmin: 2
Weight Enumerator: 1x⁰ + 0x¹ + 3x² + 0x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)⁴ (X_b)² + (X_0)⁴ (X_a)² + (X_0)⁴ (X_c)²

Dual Codewords:

Is it a nice code?: No

Generator Matrix-18

a a 0 0 0 a
b b 0 0 0 b

Codewords:

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

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

Dual Codewords:

Is it a nice code?: No

Generator Matrix-19

a a 0 0 a 0
b b 0 0 b 0

Codewords:

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

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

Dual Codewords:

Is it a nice code?: No

Generator Matrix-20

a a 0 0 a a
b b 0 0 b b

Codewords:

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

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-21

a a 0 a 0 0
b b 0 b 0 0

Codewords:

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

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

Dual Codewords:

Is it a nice code?: No

Generator Matrix-22

a a 0 a 0 a
b b 0 b 0 b

Codewords:

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

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-23

a a 0 a a 0
b b 0 b b 0

Codewords:

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

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-24

a a 0 a a a
b b 0 b b b

Codewords:

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

dmin: 5
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 0x⁴ + 3x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)¹ (X_b)⁵ + (X_0)¹ (X_a)⁵ + (X_0)¹ (X_c)⁵

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-25

a a a 0 0 0
b b b 0 0 0

Codewords:

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

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

Dual Codewords:

Is it a nice code?: No

Generator Matrix-26

a a a 0 0 a
b b b 0 0 b

Codewords:

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

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-27

a a a 0 a 0
b b b 0 b 0

Codewords:

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

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-28

a a a 0 a a
b b b 0 b b

Codewords:

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

dmin: 5
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 0x⁴ + 3x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)¹ (X_b)⁵ + (X_0)¹ (X_a)⁵ + (X_0)¹ (X_c)⁵

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-29

a a a a 0 0
b b b b 0 0

Codewords:

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

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-30

a a a a 0 a
b b b b 0 b

Codewords:

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

dmin: 5
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 0x⁴ + 3x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)¹ (X_b)⁵ + (X_0)¹ (X_a)⁵ + (X_0)¹ (X_c)⁵

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-31

a a a a a 0
b b b b b 0

Codewords:

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

dmin: 5
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 0x⁴ + 3x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)¹ (X_b)⁵ + (X_0)¹ (X_a)⁵ + (X_0)¹ (X_c)⁵

Dual Codewords:

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

Is it a nice code?: No

Generator Matrix-32

a a a a a a
b b b b b b

Codewords:

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

dmin: 6
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 0x⁴ + 0x⁵ + 3x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_b)⁶ + (X_a)⁶ + (X_c)⁶

Dual Codewords:

0 0 0 0 0 0

Generator Matrix-1

Codewords:

dmin: 1Weight Enumerator: 1x0 + 3x1 + 0x2 + 0x3 + 0x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)5 (X_b)1 + (X_0)5 (X_a)1 + (X_0)5 (X_c)1

Dual Codewords:

Is it a nice code?: Yes

Generator Matrix-2

Codewords:

dmin: 2Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3 + 0x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)4 (X_b)2 + (X_0)4 (X_a)2 + (X_0)4 (X_c)2

Dual Codewords:

Is it a nice code?: No

Generator Matrix-3

Codewords:

dmin: 2Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3 + 0x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)4 (X_b)2 + (X_0)4 (X_a)2 + (X_0)4 (X_c)2

Dual Codewords:

Is it a nice code?: No

Generator Matrix-4

Codewords:

dmin: 3Weight Enumerator: 1x0 + 0x1 + 0x2 + 3x3 + 0x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)3 (X_b)3 + (X_0)3 (X_a)3 + (X_0)3 (X_c)3

Dual Codewords:

Is it a nice code?: No

Generator Matrix-5

Codewords:

dmin: 2Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3 + 0x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)4 (X_b)2 + (X_0)4 (X_a)2 + (X_0)4 (X_c)2

Dual Codewords:

Is it a nice code?: No

Generator Matrix-6

Codewords:

dmin: 3Weight Enumerator: 1x0 + 0x1 + 0x2 + 3x3 + 0x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)3 (X_b)3 + (X_0)3 (X_a)3 + (X_0)3 (X_c)3

Dual Codewords:

Is it a nice code?: No

Generator Matrix-7

Codewords:

dmin: 3Weight Enumerator: 1x0 + 0x1 + 0x2 + 3x3 + 0x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)3 (X_b)3 + (X_0)3 (X_a)3 + (X_0)3 (X_c)3

Dual Codewords:

Is it a nice code?: No

Generator Matrix-8

Codewords:

dmin: 4Weight Enumerator: 1x0 + 0x1 + 0x2 + 0x3 + 3x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)2 (X_b)4 + (X_0)2 (X_a)4 + (X_0)2 (X_c)4

Dual Codewords:

Is it a nice code?: No

Generator Matrix-9

Codewords:

dmin: 2Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3 + 0x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)4 (X_b)2 + (X_0)4 (X_a)2 + (X_0)4 (X_c)2

Dual Codewords:

Is it a nice code?: No

Generator Matrix-10

Codewords:

dmin: 3Weight Enumerator: 1x0 + 0x1 + 0x2 + 3x3 + 0x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)3 (X_b)3 + (X_0)3 (X_a)3 + (X_0)3 (X_c)3

Dual Codewords:

Is it a nice code?: No

Generator Matrix-11

Codewords:

dmin: 3Weight Enumerator: 1x0 + 0x1 + 0x2 + 3x3 + 0x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)3 (X_b)3 + (X_0)3 (X_a)3 + (X_0)3 (X_c)3

Dual Codewords:

Is it a nice code?: No

Generator Matrix-12

Codewords:

dmin: 4Weight Enumerator: 1x0 + 0x1 + 0x2 + 0x3 + 3x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)2 (X_b)4 + (X_0)2 (X_a)4 + (X_0)2 (X_c)4

Dual Codewords:

Is it a nice code?: No

Generator Matrix-13

Codewords:

dmin: 3Weight Enumerator: 1x0 + 0x1 + 0x2 + 3x3 + 0x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)3 (X_b)3 + (X_0)3 (X_a)3 + (X_0)3 (X_c)3

Dual Codewords:

Is it a nice code?: No

Generator Matrix-14

Codewords:

dmin: 4Weight Enumerator: 1x0 + 0x1 + 0x2 + 0x3 + 3x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)2 (X_b)4 + (X_0)2 (X_a)4 + (X_0)2 (X_c)4

Dual Codewords:

Is it a nice code?: No

Generator Matrix-15

Codewords:

dmin: 4Weight Enumerator: 1x0 + 0x1 + 0x2 + 0x3 + 3x4 + 0x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)2 (X_b)4 + (X_0)2 (X_a)4 + (X_0)2 (X_c)4

Dual Codewords:

Is it a nice code?: No

Generator Matrix-16

Codewords:

dmin: 5Weight Enumerator: 1x0 + 0x1 + 0x2 + 0x3 + 0x4 + 3x5 + 0x6Complete Weight Enumerator: (X_0)6 + (X_0)1 (X_b)5 + (X_0)1 (X_a)5 + (X_0)1 (X_c)5

Dual Codewords:

Is it a nice code?: No

dmin: 1
Weight Enumerator: 1x⁰ + 3x¹ + 0x² + 0x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)⁵ (X_b)¹ + (X_0)⁵ (X_a)¹ + (X_0)⁵ (X_c)¹

dmin: 2
Weight Enumerator: 1x⁰ + 0x¹ + 3x² + 0x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)⁴ (X_b)² + (X_0)⁴ (X_a)² + (X_0)⁴ (X_c)²

dmin: 2
Weight Enumerator: 1x⁰ + 0x¹ + 3x² + 0x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)⁴ (X_b)² + (X_0)⁴ (X_a)² + (X_0)⁴ (X_c)²

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

dmin: 2
Weight Enumerator: 1x⁰ + 0x¹ + 3x² + 0x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)⁴ (X_b)² + (X_0)⁴ (X_a)² + (X_0)⁴ (X_c)²

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

dmin: 2
Weight Enumerator: 1x⁰ + 0x¹ + 3x² + 0x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)⁴ (X_b)² + (X_0)⁴ (X_a)² + (X_0)⁴ (X_c)²

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

dmin: 5
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 0x⁴ + 3x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)¹ (X_b)⁵ + (X_0)¹ (X_a)⁵ + (X_0)¹ (X_c)⁵

dmin: 2
Weight Enumerator: 1x⁰ + 0x¹ + 3x² + 0x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)⁴ (X_b)² + (X_0)⁴ (X_a)² + (X_0)⁴ (X_c)²

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

dmin: 5
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 0x⁴ + 3x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)¹ (X_b)⁵ + (X_0)¹ (X_a)⁵ + (X_0)¹ (X_c)⁵

dmin: 3
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 3x³ + 0x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)³ (X_b)³ + (X_0)³ (X_a)³ + (X_0)³ (X_c)³

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

dmin: 5
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 0x⁴ + 3x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)¹ (X_b)⁵ + (X_0)¹ (X_a)⁵ + (X_0)¹ (X_c)⁵

dmin: 4
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 3x⁴ + 0x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)² (X_b)⁴ + (X_0)² (X_a)⁴ + (X_0)² (X_c)⁴

dmin: 5
Weight Enumerator: 1x⁰ + 0x¹ + 0x² + 0x³ + 0x⁴ + 3x⁵ + 0x⁶
Complete Weight Enumerator: (X_0)⁶ + (X_0)¹ (X_b)⁵ + (X_0)¹ (X_a)⁵ + (X_0)¹ (X_c)⁵