n=3, k0=2, k1=0
Optimal Minimum Distance: 2
Generator Matrices that generate Codes having Optimal Minimum Distance: 4,
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 a 0
b 0 0
0 b 0
Codewords:
0 0 0
0 b 0
b 0 0
b b 0
0 a 0
0 c 0
b a 0
b c 0
a 0 0
a b 0
c 0 0
c b 0
a a 0
a c 0
c a 0
c c 0
dmin: 1
Weight Enumerator: 1x0 + 6x1 + 9x2 + 0x3
Complete Weight Enumerator: (X_0)3 + (X_0)2 (X_b)1 + (X_0)2 (X_b)1 + (X_0)1 (X_b)2 + (X_0)2 (X_a)1 + (X_0)2 (X_c)1 + (X_0)1 (X_a)1 (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_b)1 + (X_0)2 (X_c)1 + (X_0)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)2 + (X_0)1 (X_a)1 (X_c)1 + (X_0)1 (X_a)1 (X_c)1 + (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?: Yes
Generator Matrix-2
a 0 0
0 a a
b 0 0
0 b b
Codewords:
0 0 0
0 b b
b 0 0
b b b
0 a a
0 c c
b a a
b c c
a 0 0
a b b
c 0 0
c b b
a a a
a c c
c a a
c c c
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 3x2 + 9x3
Complete Weight Enumerator: (X_0)3 + (X_0)1 (X_b)2 + (X_0)2 (X_b)1 + (X_b)3 + (X_0)1 (X_a)2 + (X_0)1 (X_c)2 + (X_a)2 (X_b)1 + (X_b)1 (X_c)2 + (X_0)2 (X_a)1 + (X_a)1 (X_b)2 + (X_0)2 (X_c)1 + (X_b)2 (X_c)1 + (X_a)3 + (X_a)1 (X_c)2 + (X_a)2 (X_c)1 + (X_c)3
Dual Codewords:
0 0 0
Is it a nice code?: No
Generator Matrix-3
a 0 a
0 a 0
b 0 b
0 b 0
Codewords:
0 0 0
0 b 0
b 0 b
b b b
0 a 0
0 c 0
b a b
b c b
a 0 a
a b a
c 0 c
c b c
a a a
a c a
c a c
c c c
dmin: 1
Weight Enumerator: 1x0 + 3x1 + 3x2 + 9x3
Complete Weight Enumerator: (X_0)3 + (X_0)2 (X_b)1 + (X_0)1 (X_b)2 + (X_b)3 + (X_0)2 (X_a)1 + (X_0)2 (X_c)1 + (X_a)1 (X_b)2 + (X_b)2 (X_c)1 + (X_0)1 (X_a)2 + (X_a)2 (X_b)1 + (X_0)1 (X_c)2 + (X_b)1 (X_c)2 + (X_a)3 + (X_a)2 (X_c)1 + (X_a)1 (X_c)2 + (X_c)3
Dual Codewords:
0 0 0
Is it a nice code?: No
Generator Matrix-4
a 0 a
0 a a
b 0 b
0 b b
Codewords:
0 0 0
0 b b
b 0 b
b b 0
0 a a
0 c c
b a c
b c a
a 0 a
a b c
c 0 c
c b a
a a 0
a c b
c a b
c c 0
dmin: 2
Weight Enumerator: 1x0 + 0x1 + 9x2 + 6x3
Complete Weight Enumerator: (X_0)3 + (X_0)1 (X_b)2 + (X_0)1 (X_b)2 + (X_0)1 (X_b)2 + (X_0)1 (X_a)2 + (X_0)1 (X_c)2 + (X_a)1 (X_b)1 (X_c)1 + (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_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_a)2 + (X_a)1 (X_b)1 (X_c)1 + (X_a)1 (X_b)1 (X_c)1 + (X_0)1 (X_c)2
Dual Codewords:
0 0 0
Is it a nice code?: No