Code2

Database for the paper “Ruowen Liu, Shitao Li, Minjia Shi, Construction of linear codes with various Hermitian hull dimensions and related EAQECCs, Advances in Mathematics of Communications, 2024, Doi: 10.3934/amc.2024013.”

Quaternary linear codes with two-dimensional hull (h=2)

n=4

[4, 2, 2] Quasicyclic of degree 2 Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 1]
[ 0 1 1 0]
_______________

n=5

[5, 2, 4] Cyclic Linear Code over GF(2^2)
Generator matrix:
[ 1 0 1 w w]
[ 0 1 w w 1]
[5, 3, 3] Cyclic Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 1 w^2]
[ 0 1 0 w^2 w^2]
[ 0 0 1 w^2 1]
_______________

n=6

[6, 2, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 1 w^2 w^2]
[ 0 1 0 w^2 w^2 1]

[6, 3, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 1 w^2 w^2]
[ 0 1 0 0 1 1]
[ 0 0 1 1 0 w^2]

[6, 4, 2] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 1 w]
[ 0 1 0 0 w^2 1]
[ 0 0 1 0 0 1]
[ 0 0 0 1 w^2 0]
_______________

n=7

[7, 2, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 1 w^2 w^2 0]
[ 0 1 0 w^2 w^2 1 0]

[7, 3, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 w^2 w^2 w 1]
[ 0 1 0 0 1 1 1]
[ 0 0 1 1 1 w w^2]

[7, 4, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 1 w^2 w]
[ 0 1 0 0 w 1 w]
[ 0 0 1 0 0 1 1]
[ 0 0 0 1 1 0 w^2]

[7, 5, 2] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 1]
[ 0 1 0 0 0 1 w^2]
[ 0 0 1 0 0 w^2 1]
[ 0 0 0 1 0 0 w]
[ 0 0 0 0 1 w^2 w^2]
_______________

n=8

[8, 2, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 1 w^2 w^2 w 0 w]
[ 0 1 w w 0 w^2 w^2 1]

[8, 3, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 w^2 w 0 1 1]
[ 0 1 0 0 1 1 1 1]
[ 0 0 1 1 0 1 1 w]

[8, 4, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 w w 0 w^2]
[ 0 1 0 0 1 1 1 w^2]
[ 0 0 1 0 0 1 1 1]
[ 0 0 0 1 1 0 1 1]

[8, 5, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 w^2 1 1]
[ 0 1 0 0 0 w 0 1]
[ 0 0 1 0 0 w^2 1 w]
[ 0 0 0 1 0 0 1 1]
[ 0 0 0 0 1 1 1 w]

[8, 6, 2] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 w^2 1]
[ 0 1 0 0 0 0 w 1]
[ 0 0 1 0 0 0 1 0]
[ 0 0 0 1 0 0 w^2 1]
[ 0 0 0 0 1 0 0 1]
[ 0 0 0 0 0 1 w^2 w]
_______________

n=9

[9, 2, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 1 w^2 w^2 w 0 w 0]
[ 0 1 w w 0 w^2 w^2 1 0]

[9, 3, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 w^2 w 0 1 1 0]
[ 0 1 0 0 1 1 1 1 0]
[ 0 0 1 1 0 1 1 w 0]

[9, 4, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 w w w^2 1 w]
[ 0 1 0 0 w^2 w 0 1 1]
[ 0 0 1 0 0 1 1 1 1]
[ 0 0 0 1 1 0 1 1 w]

[9, 5, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 1 w^2 w 1]
[ 0 1 0 0 0 w w 0 w^2]
[ 0 0 1 0 0 0 w w^2 1]
[ 0 0 0 1 0 0 1 1 1]
[ 0 0 0 0 1 1 w w w^2]

[9, 6, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 w^2 1]
[ 0 1 0 0 0 0 0 1 w^2]
[ 0 0 1 0 0 0 w^2 w w^2]
[ 0 0 0 1 0 0 w^2 1 w]
[ 0 0 0 0 1 0 0 1 1]
[ 0 0 0 0 0 1 1 1 w]

[9, 7, 2] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 w^2]
[ 0 1 0 0 0 0 0 1 w^2]
[ 0 0 1 0 0 0 0 0 w]
[ 0 0 0 1 0 0 0 1 w]
[ 0 0 0 0 1 0 0 w^2 w^2]
[ 0 0 0 0 0 1 0 1 w^2]
[ 0 0 0 0 0 0 1 w^2 w]
_______________

n=10

[10, 2, 8] Cyclic Linear Code over GF(2^2)
Generator matrix:
[ 1 0 1 w w 1 0 1 w w]
[ 0 1 w w 1 0 1 w w 1]

[10, 3, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 1 1 1 1 w w^2 0]
[ 0 1 0 1 w^2 w^2 1 0 1 w^2]
[ 0 0 1 w^2 w^2 1 0 1 w^2 w^2]

[10, 4, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 w 1 0 1 w^2 w^2]
[ 0 1 0 0 w^2 1 w^2 w w^2 0]
[ 0 0 1 0 0 1 1 1 1 1]
[ 0 0 0 1 1 0 1 1 w w^2]

[10, 5, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 w^2 w 1 w^2 0]
[ 0 1 0 0 0 w^2 1 1 0 w]
[ 0 0 1 0 0 w^2 w 0 1 1]
[ 0 0 0 1 0 0 1 1 1 1]
[ 0 0 0 0 1 1 0 1 1 w]

[10, 6, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 w w^2 1 w]
[ 0 1 0 0 0 0 w w^2 w 0]
[ 0 0 1 0 0 0 w^2 w^2 0 w]
[ 0 0 0 1 0 0 1 1 w w]
[ 0 0 0 0 1 0 0 1 1 1]
[ 0 0 0 0 0 1 1 w w w^2]

[10, 7, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 w^2 1 0]
[ 0 1 0 0 0 0 0 1 w 1]
[ 0 0 1 0 0 0 0 0 w^2 w]
[ 0 0 0 1 0 0 0 1 w^2 1]
[ 0 0 0 0 1 0 0 w w^2 w^2]
[ 0 0 0 0 0 1 0 0 1 1]
[ 0 0 0 0 0 0 1 1 1 w]

[10, 8, 2] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 0 1]
[ 0 1 0 0 0 0 0 0 1 1]
[ 0 0 1 0 0 0 0 0 w w^2]
[ 0 0 0 1 0 0 0 0 1 1]
[ 0 0 0 0 1 0 0 0 1 w]
[ 0 0 0 0 0 1 0 0 1 w^2]
[ 0 0 0 0 0 0 1 0 1 0]
[ 0 0 0 0 0 0 0 1 w 1]
_______________

n=11

[11, 2, 8] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 1 w w 1 0 1 w w 0]
[ 0 1 w w 1 0 1 w w 1 0]

[11, 3, 7] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 w 1 w w 1 w^2 w^2 w^2]
[ 0 1 0 w 0 1 w w 0 w^2 1]
[ 0 0 1 0 w^2 w^2 w 0 1 1 w^2]

[11, 4, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 w w 1 w w w^2 w]
[ 0 1 0 0 w w^2 w w^2 w w 1]
[ 0 0 1 0 w w^2 1 0 w^2 w 0]
[ 0 0 0 1 0 1 w^2 w^2 w^2 0 w^2]

[11, 5, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 w 0 1 w^2 1 w 0]
[ 0 1 0 0 w 0 w 1 w^2 0 w]
[ 0 0 1 0 w 0 1 w w 0 w^2]
[ 0 0 0 1 0 0 w^2 0 1 w^2 w]
[ 0 0 0 0 0 1 0 w^2 w w^2 1]

[11, 6, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 w w^2 1 w 0]
[ 0 1 0 0 0 0 w w^2 w 0 0]
[ 0 0 1 0 0 0 w^2 w^2 0 w 0]
[ 0 0 0 1 0 0 1 1 w w 0]
[ 0 0 0 0 1 0 0 1 1 1 0]
[ 0 0 0 0 0 1 1 w w w^2 0]

[11, 7, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 1 0 w^2 w]
[ 0 1 0 0 0 0 0 1 0 1 1]
[ 0 0 1 0 0 0 0 1 1 w 0]
[ 0 0 0 1 0 0 0 1 w 1 w]
[ 0 0 0 0 1 0 0 0 w w^2 1]
[ 0 0 0 0 0 1 0 0 1 1 1]
[ 0 0 0 0 0 0 1 1 w w w^2]

[11, 8, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 w 0 1]
[ 0 1 0 0 0 0 0 0 0 w w^2]
[ 0 0 1 0 0 0 0 0 1 w^2 0]
[ 0 0 0 1 0 0 0 0 w 0 w]
[ 0 0 0 0 1 0 0 0 w 0 w^2]
[ 0 0 0 0 0 1 0 0 w w^2 w^2]
[ 0 0 0 0 0 0 1 0 0 1 1]
[ 0 0 0 0 0 0 0 1 1 1 w]

[11, 9, 2] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 0 w^2 w^2]
[ 0 1 0 0 0 0 0 0 0 0 w^2]
[ 0 0 1 0 0 0 0 0 0 w^2 1]
[ 0 0 0 1 0 0 0 0 0 1 w^2]
[ 0 0 0 0 1 0 0 0 0 w 1]
[ 0 0 0 0 0 1 0 0 0 w w]
[ 0 0 0 0 0 0 1 0 0 w w]
[ 0 0 0 0 0 0 0 1 0 0 1]
[ 0 0 0 0 0 0 0 0 1 1 w^2]
_______________

n=12

[12, 2, 8] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 1 w w 1 0 1 w w 0 0]
[ 0 1 w w 1 0 1 w w 1 0 0]

[12, 3, 8] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 1 1 w 0 1 w w^2 w 1]
[ 0 1 0 w 1 w^2 1 0 1 1 w w^2]
[ 0 0 1 1 1 1 1 w 1 0 w^2 w]

[12, 4, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 w^2 0 w w 1 1 0 w]
[ 0 1 0 0 w^2 0 w^2 1 w^2 w^2 w 0]
[ 0 0 1 0 w^2 0 w w^2 w 0 0 1]
[ 0 0 0 1 1 0 0 w^2 w^2 1 w w^2]

[12, 5, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 1 0 0 w^2 w 1 w^2 0 w^2]
[ 0 1 0 1 0 0 w 0 w^2 1 w w]
[ 0 0 1 w 0 0 1 w 0 w^2 1 0]
[ 0 0 0 0 1 0 1 w 1 w 1 w^2]
[ 0 0 0 0 0 1 1 w^2 w^2 1 w w^2]

[12, 6, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 1 w^2 1 0 w^2 0]
[ 0 1 0 0 0 0 0 1 w^2 1 0 w^2]
[ 0 0 1 0 0 0 w w^2 w^2 w^2 w w]
[ 0 0 0 1 0 0 1 0 w w^2 1 w^2]
[ 0 0 0 0 1 0 w w w w 0 w^2]
[ 0 0 0 0 0 1 w 1 0 w 1 w]

[12, 7, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 1 0 w^2 w 0]
[ 0 1 0 0 0 0 0 1 0 1 1 0]
[ 0 0 1 0 0 0 0 1 1 w 0 0]
[ 0 0 0 1 0 0 0 1 w 1 w 0]
[ 0 0 0 0 1 0 0 0 w w^2 1 0]
[ 0 0 0 0 0 1 0 0 1 1 1 0]
[ 0 0 0 0 0 0 1 1 w w w^2 0]

[12, 8, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 1 0 1 w^2]
[ 0 1 0 0 0 0 0 0 1 1 0 w^2]
[ 0 0 1 0 0 0 0 0 w 0 w^2 w^2]
[ 0 0 0 1 0 0 0 0 1 1 w 0]
[ 0 0 0 0 1 0 0 0 1 w 1 w]
[ 0 0 0 0 0 1 0 0 0 w w^2 1]
[ 0 0 0 0 0 0 1 0 0 1 1 1]
[ 0 0 0 0 0 0 0 1 1 w w w^2]

[12, 9, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 0 w 1 w]
[ 0 1 0 0 0 0 0 0 0 1 w 1]
[ 0 0 1 0 0 0 0 0 0 w^2 w^2 w^2]
[ 0 0 0 1 0 0 0 0 0 w 1 0]
[ 0 0 0 0 1 0 0 0 0 w^2 w 1]
[ 0 0 0 0 0 1 0 0 0 w 0 1]
[ 0 0 0 0 0 0 1 0 0 w^2 1 w]
[ 0 0 0 0 0 0 0 1 0 0 1 1]
[ 0 0 0 0 0 0 0 0 1 1 1 w]

[12, 10, 2] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 0 0 w^2 1]
[ 0 1 0 0 0 0 0 0 0 0 1 w^2]
[ 0 0 1 0 0 0 0 0 0 0 1 w]
[ 0 0 0 1 0 0 0 0 0 0 1 w]
[ 0 0 0 0 1 0 0 0 0 0 w w^2]
[ 0 0 0 0 0 1 0 0 0 0 w w]
[ 0 0 0 0 0 0 1 0 0 0 1 w^2]
[ 0 0 0 0 0 0 0 1 0 0 w 0]
[ 0 0 0 0 0 0 0 0 1 0 0 w]
[ 0 0 0 0 0 0 0 0 0 1 w w]
_______________

n=13

[13, 2, 10] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 1 0 0 w^2 1 w^2 w^2 w^2 w^2 1 w^2]
[ 0 1 w^2 1 w 0 w 1 w w^2 1 0 w]

[13, 3, 9] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 w^2 1 w w^2 0 1 w^2 0 1 w]
[ 0 1 0 0 1 1 1 w w w w^2 w^2 w^2]
[ 0 0 1 1 1 1 1 1 1 1 1 1 1]

[13, 4, 8] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 w^2 w 1 w^2 1 0 1 w^2 1]
[ 0 1 0 0 w w^2 w^2 w^2 0 w w 0 w^2]
[ 0 0 1 0 w^2 1 0 0 w w^2 w w w]
[ 0 0 0 1 w 0 1 w w^2 w^2 w 1 0]

[13, 5, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 1 0 0 w 0 w 1 1 0]
[ 0 1 0 0 1 0 0 0 1 w^2 1 0 w^2]
[ 0 0 1 0 w 0 0 1 w^2 1 0 w w]
[ 0 0 0 1 w 0 0 w^2 w^2 w w 1 1]
[ 0 0 0 0 0 1 0 0 w w 1 w^2 1]

[13, 6, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 w 0 w w^2 1 0 0 w]
[ 0 1 0 0 0 1 0 0 w^2 w^2 w^2 0 w^2]
[ 0 0 1 0 0 w^2 0 0 w w^2 0 w w^2]
[ 0 0 0 1 0 w^2 0 w w^2 w 0 w^2 0]
[ 0 0 0 0 1 1 0 w 0 w^2 w w^2 w^2]
[ 0 0 0 0 0 0 1 0 w w 1 w^2 1]

[13, 7, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 0 1 w^2 1 w^2]
[ 0 1 0 0 0 0 w 0 1 0 w^2 0 w]
[ 0 0 1 0 0 0 0 0 1 0 1 1 w]
[ 0 0 0 1 0 0 w^2 0 0 w 1 w^2 w]
[ 0 0 0 0 1 0 w 0 w^2 w w 0 w]
[ 0 0 0 0 0 1 1 0 w^2 w 1 1 0]
[ 0 0 0 0 0 0 0 1 w 1 w 1 w]

[13, 8, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 w w^2 0 w 1]
[ 0 1 0 0 0 0 0 0 w w^2 1 w 0]
[ 0 0 1 0 0 0 0 0 w 1 w^2 w^2 w^2]
[ 0 0 0 1 0 0 0 0 w^2 1 w^2 w 1]
[ 0 0 0 0 1 0 0 0 w 1 0 w w^2]
[ 0 0 0 0 0 1 0 0 1 1 1 w w^2]
[ 0 0 0 0 0 0 1 0 w^2 w^2 1 0 1]
[ 0 0 0 0 0 0 0 1 w^2 w^2 w w^2 1]

[13, 9, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 0 w^2 0 w^2 1]
[ 0 1 0 0 0 0 0 0 0 w w 0 w]
[ 0 0 1 0 0 0 0 0 0 w 0 w^2 w]
[ 0 0 0 1 0 0 0 0 0 w^2 w w^2 w]
[ 0 0 0 0 1 0 0 0 0 0 w^2 w 1]
[ 0 0 0 0 0 1 0 0 0 w w 1 1]
[ 0 0 0 0 0 0 1 0 0 1 1 w w]
[ 0 0 0 0 0 0 0 1 0 0 1 1 1]
[ 0 0 0 0 0 0 0 0 1 1 w w w^2]

[13, 10, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 0 0 1 w^2 w]
[ 0 1 0 0 0 0 0 0 0 0 w^2 1 0]
[ 0 0 1 0 0 0 0 0 0 0 1 w^2 w^2]
[ 0 0 0 1 0 0 0 0 0 0 1 w^2 0]
[ 0 0 0 0 1 0 0 0 0 0 1 w 1]
[ 0 0 0 0 0 1 0 0 0 0 0 w^2 w]
[ 0 0 0 0 0 0 1 0 0 0 1 w^2 1]
[ 0 0 0 0 0 0 0 1 0 0 w w^2 w^2]
[ 0 0 0 0 0 0 0 0 1 0 0 1 1]
[ 0 0 0 0 0 0 0 0 0 1 1 1 w]

[13, 11, 2] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 0 0 w 0 w^2]
[ 0 1 0 0 0 0 0 0 0 0 0 0 w^2]
[ 0 0 1 0 0 0 0 0 0 0 1 0 1]
[ 0 0 0 1 0 0 0 0 0 0 w 0 w^2]
[ 0 0 0 0 1 0 0 0 0 0 w^2 0 0]
[ 0 0 0 0 0 1 0 0 0 0 w^2 0 0]
[ 0 0 0 0 0 0 1 0 0 0 w 0 w]
[ 0 0 0 0 0 0 0 1 0 0 1 0 1]
[ 0 0 0 0 0 0 0 0 1 0 w 0 1]
[ 0 0 0 0 0 0 0 0 0 1 1 0 w]
[ 0 0 0 0 0 0 0 0 0 0 0 1 w^2]

**********************

Quaternary linear codes with three-dimensional hull (h=3)

n=6

[6, 3, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 1 w^2 w^2]
[ 0 1 0 w^2 w^2 1]
[ 0 0 1 w^2 1 w^2]
_______________

n=7

[7, 3, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 w^2 w^2 0 w^2]
[ 0 1 0 0 1 1 1]
[ 0 0 1 1 0 1 1]

[7, 4, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 1 w^2 0]
[ 0 1 0 0 1 w^2 w^2]
[ 0 0 1 0 0 1 1]
[ 0 0 0 1 1 0 w^2]
_______________

n=8

[8, 3, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 w^2 w^2 0 w^2 0]
[ 0 1 0 0 1 1 1 0]
[ 0 0 1 1 0 1 1 0]

[8, 4, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 1 w 0 w]
[ 0 1 0 0 1 w^2 w 1]
[ 0 0 1 0 0 1 1 1]
[ 0 0 0 1 1 1 w w^2]

[8, 5, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 1 w^2]
[ 0 1 0 0 0 w^2 w w^2]
[ 0 0 1 0 0 w^2 1 w]
[ 0 0 0 1 0 0 1 1]
[ 0 0 0 0 1 1 1 w]
_______________

n=9

[9, 3, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 w^2 w^2 1 w^2 1 0]
[ 0 1 0 0 1 1 1 1 1]
[ 0 0 1 1 0 w w w^2 w^2]

[9, 4, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 1 w 0 w 0]
[ 0 1 0 0 1 w^2 w 1 0]
[ 0 0 1 0 0 1 1 1 0]
[ 0 0 0 1 1 1 w w^2 0]

[9, 5, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 w^2 w 0 w^2]
[ 0 1 0 0 0 0 w w^2 1]
[ 0 0 1 0 0 1 1 w w]
[ 0 0 0 1 0 0 1 1 1]
[ 0 0 0 0 1 1 w w w^2]

[9, 6, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 w w 0]
[ 0 1 0 0 0 0 w^2 1 1]
[ 0 0 1 0 0 0 w 0 1]
[ 0 0 0 1 0 0 w^2 1 w]
[ 0 0 0 0 1 0 0 1 1]
[ 0 0 0 0 0 1 1 1 w]
_______________

n=10

[10, 3, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 w^2 w^2 1 w^2 1 0 0]
[ 0 1 0 0 1 1 1 1 1 0]
[ 0 0 1 1 0 w w w^2 w^2 0]

[10, 4, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 1 0 w w^2 w^2]
[ 0 1 0 0 w^2 0 0 w 1 w^2]
[ 0 0 1 0 1 w w 1 0 w^2]
[ 0 0 0 1 w w 1 w^2 w^2 w]

[10, 5, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 w^2 w 0 w^2 0]
[ 0 1 0 0 0 0 w w^2 1 0]
[ 0 0 1 0 0 1 1 w w 0]
[ 0 0 0 1 0 0 1 1 1 0]
[ 0 0 0 0 1 1 w w w^2 0]

[10, 6, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 w w 0 0]
[ 0 1 0 0 0 0 w^2 1 1 0]
[ 0 0 1 0 0 0 w 0 1 0]
[ 0 0 0 1 0 0 w^2 1 w 0]
[ 0 0 0 0 1 0 0 1 1 0]
[ 0 0 0 0 0 1 1 1 w 0]

[10, 7, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 w^2 w w]
[ 0 1 0 0 0 0 0 0 w^2 w]
[ 0 0 1 0 0 0 0 w 0 w]
[ 0 0 0 1 0 0 0 w 0 w^2]
[ 0 0 0 0 1 0 0 w w^2 w^2]
[ 0 0 0 0 0 1 0 0 1 1]
[ 0 0 0 0 0 0 1 1 1 w]
_______________

n=11

[11, 3, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 w^2 w^2 1 w^2 1 0 0 0]
[ 0 1 0 0 1 1 1 1 1 0 0]
[ 0 0 1 1 0 w w w^2 w^2 0 0]

[11, 4, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 1 w w^2 w 1 w^2 1]
[ 0 1 0 0 1 1 1 1 w w^2 0]
[ 0 0 1 0 1 w^2 w^2 1 0 1 w^2]
[ 0 0 0 1 w^2 w^2 1 0 1 w^2 w^2]

[11, 5, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 w 0 w w^2 w^2 0]
[ 0 1 0 0 0 w w^2 1 1 1 1]
[ 0 0 1 0 0 0 w w w^2 1 w]
[ 0 0 0 1 0 1 w w 1 0 w^2]
[ 0 0 0 0 1 w w 1 w^2 w^2 w]

[11, 6, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 w 0 w 1 w^2 1]
[ 0 1 0 0 0 0 0 1 w w^2 w]
[ 0 0 1 0 0 0 0 w^2 w 0 w^2]
[ 0 0 0 1 0 1 0 0 w^2 w 0]
[ 0 0 0 0 1 1 0 1 0 w^2 w^2]
[ 0 0 0 0 0 0 1 1 w w w^2]

[11, 7, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 w^2 w^2 w^2 1]
[ 0 1 0 0 0 0 0 w w^2 w w]
[ 0 0 1 0 0 0 0 1 w w^2 0]
[ 0 0 0 1 0 0 0 1 0 w^2 w]
[ 0 0 0 0 1 0 0 0 w 1 w^2]
[ 0 0 0 0 0 1 0 0 1 1 1]
[ 0 0 0 0 0 0 1 0 1 w w^2]

[11, 8, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 1 w 1]
[ 0 1 0 0 0 0 0 0 w^2 w^2 w^2]
[ 0 0 1 0 0 0 0 0 w 1 0]
[ 0 0 0 1 0 0 0 0 w^2 w 1]
[ 0 0 0 0 1 0 0 0 w 0 1]
[ 0 0 0 0 0 1 0 0 w^2 1 w]
[ 0 0 0 0 0 0 1 0 0 1 1]
[ 0 0 0 0 0 0 0 1 1 1 w]
_______________

n=12

[12, 3, 8] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 w w^2 w w^2 w w 1 w w]
[ 0 1 0 w w^2 1 0 w^2 w 0 w^2 w^2]
[ 0 0 1 0 1 w^2 w^2 w^2 0 w^2 w w]

[12, 4, 7] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 w 0 w 1 w^2 0 w 0 1]
[ 0 1 0 w 0 1 w w 0 w^2 1 0]
[ 0 0 1 0 0 w^2 0 1 w^2 w 1 w^2]
[ 0 0 0 0 1 0 w^2 w w^2 1 w^2 1]

[12, 5, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 w^2 w^2 0 w w^2 0 1]
[ 0 1 0 0 0 w w 1 w w w^2 w]
[ 0 0 1 0 0 w w^2 w w^2 w w 1]
[ 0 0 0 1 0 w w^2 1 0 w^2 w 0]
[ 0 0 0 0 1 0 1 w^2 w^2 w^2 0 w^2]

[12, 6, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 w 1 w^2 w w 1]
[ 0 1 0 0 0 0 w^2 w 0 1 1 w^2]
[ 0 0 1 0 0 0 w 0 1 w^2 1 w]
[ 0 0 0 1 0 0 w w w 0 0 1]
[ 0 0 0 0 1 0 w w^2 1 0 w^2 w]
[ 0 0 0 0 0 1 0 w w^2 1 w w]

[12, 7, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 w 0 1 1 0 1]
[ 0 1 0 0 0 0 1 0 w^2 w w^2 0]
[ 0 0 1 0 0 0 w 0 w 0 0 w]
[ 0 0 0 1 0 0 w^2 0 1 w^2 w 0]
[ 0 0 0 0 1 0 w 0 0 w^2 1 w]
[ 0 0 0 0 0 1 0 0 w 1 w^2 w]
[ 0 0 0 0 0 0 0 1 0 w^2 w^2 w^2]

[12, 8, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 w w 0 w]
[ 0 1 0 0 0 0 0 0 w 0 w^2 w]
[ 0 0 1 0 0 0 0 0 w^2 w w^2 w]
[ 0 0 0 1 0 0 0 0 0 w^2 w 1]
[ 0 0 0 0 1 0 0 0 w w 1 1]
[ 0 0 0 0 0 1 0 0 1 1 w w]
[ 0 0 0 0 0 0 1 0 0 1 1 1]
[ 0 0 0 0 0 0 0 1 1 w w w^2]

[12, 9, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 0 1 0 w]
[ 0 1 0 0 0 0 0 0 0 w w^2 0]
[ 0 0 1 0 0 0 0 0 0 0 w w^2]
[ 0 0 0 1 0 0 0 0 0 w^2 w 0]
[ 0 0 0 0 1 0 0 0 0 1 1 w]
[ 0 0 0 0 0 1 0 0 0 1 w^2 w]
[ 0 0 0 0 0 0 1 0 0 w 1 w]
[ 0 0 0 0 0 0 0 1 0 0 1 1]
[ 0 0 0 0 0 0 0 0 1 1 0 w^2]
_______________

n=13

[13, 3, 8] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 w w^2 w w^2 w w 1 w w 0]
[ 0 1 0 w w^2 1 0 w^2 w 0 w^2 w^2 0]
[ 0 0 1 0 1 w^2 w^2 w^2 0 w^2 w w 0]

[13, 4, 7] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 1 1 w 0 w 1 w w^2 0]
[ 0 1 0 0 1 0 1 w w^2 w^2 w 1 0]
[ 0 0 1 0 0 w^2 w^2 w^2 w^2 1 w^2 0 0]
[ 0 0 0 1 w^2 w^2 1 w^2 0 0 w 1 0]

[13, 5, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 w^2 0 w^2 w w w 0]
[ 0 1 0 0 0 0 0 w w w^2 0 w^2 w^2]
[ 0 0 1 0 0 0 1 w^2 w w^2 1 0 0]
[ 0 0 0 1 0 0 1 w w^2 w 1 1 w^2]
[ 0 0 0 0 1 0 1 w w 1 0 1 w]

[13, 6, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 w^2 0 1 0 w^2 w w 0]
[ 0 1 0 0 0 1 0 w w w^2 1 0 w^2]
[ 0 0 1 0 0 w 0 0 1 w w w w]
[ 0 0 0 1 0 w 0 w w^2 w w^2 1 w^2]
[ 0 0 0 0 1 w^2 0 w^2 w^2 0 1 1 w^2]
[ 0 0 0 0 0 0 1 w 1 w 1 w w^2]

[13, 7, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 w^2 w^2 w^2 0 0 1]
[ 0 1 0 0 0 0 0 0 1 0 w^2 1 w^2]
[ 0 0 1 0 0 0 0 1 0 1 1 w 0]
[ 0 0 0 1 0 0 0 w^2 w^2 0 0 w w^2]
[ 0 0 0 0 1 0 0 0 1 w^2 1 0 w^2]
[ 0 0 0 0 0 1 0 1 w w^2 1 w^2 0]
[ 0 0 0 0 0 0 1 1 w^2 w 0 1 1]

[13, 8, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 w w 0 w 0]
[ 0 1 0 0 0 0 0 0 w 0 w^2 w 0]
[ 0 0 1 0 0 0 0 0 w^2 w w^2 w 0]
[ 0 0 0 1 0 0 0 0 0 w^2 w 1 0]
[ 0 0 0 0 1 0 0 0 w w 1 1 0]
[ 0 0 0 0 0 1 0 0 1 1 w w 0]
[ 0 0 0 0 0 0 1 0 0 1 1 1 0]
[ 0 0 0 0 0 0 0 1 1 w w w^2 0]

[13, 9, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 0 w^2 w^2 w 1]
[ 0 1 0 0 0 0 0 0 0 1 0 w^2 w^2]
[ 0 0 1 0 0 0 0 0 0 w 0 w w^2]
[ 0 0 0 1 0 0 0 0 0 w 0 w^2 w]
[ 0 0 0 0 1 0 0 0 0 w^2 w w^2 w^2]
[ 0 0 0 0 0 1 0 0 0 w^2 1 1 0]
[ 0 0 0 0 0 0 1 0 0 w^2 w 1 1]
[ 0 0 0 0 0 0 0 1 0 0 1 1 1]
[ 0 0 0 0 0 0 0 0 1 1 1 w w^2]

[13, 10, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 0 0 0 w^2 1]
[ 0 1 0 0 0 0 0 0 0 0 w w^2 w^2]
[ 0 0 1 0 0 0 0 0 0 0 1 w^2 0]
[ 0 0 0 1 0 0 0 0 0 0 w w 1]
[ 0 0 0 0 1 0 0 0 0 0 w^2 0 w^2]
[ 0 0 0 0 0 1 0 0 0 0 0 1 w^2]
[ 0 0 0 0 0 0 1 0 0 0 w^2 w w^2]
[ 0 0 0 0 0 0 0 1 0 0 w^2 1 w]
[ 0 0 0 0 0 0 0 0 1 0 0 1 1]
[ 0 0 0 0 0 0 0 0 0 1 1 1 w]

**********************

Quaternary linear codes with four-dimensional hull (h=4)

n=8

[8, 4, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 1 1 1 0]
[ 0 1 0 0 w^2 w^2 0 w^2]
[ 0 0 1 0 0 1 1 1]
[ 0 0 0 1 1 0 1 1]
_______________

n=9

[9, 4, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 w 0 w w^2 w^2 1]
[ 0 1 0 w^2 0 1 0 0 1]
[ 0 0 1 0 0 w^2 w^2 0 w^2]
[ 0 0 0 0 1 1 0 1 1]

[9, 5, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 1 w^2 w^2 0]
[ 0 1 0 0 0 w w^2 w w^2]
[ 0 0 1 0 0 1 0 w^2 w^2]
[ 0 0 0 1 0 1 0 w^2 0]
[ 0 0 0 0 1 w^2 w^2 1 w^2]
_______________

n=10

[10, 4, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 w w w^2 w 1]
[ 0 1 0 0 w w^2 1 0 w^2 w^2]
[ 0 0 1 0 1 w w^2 1 w 0]
[ 0 0 0 1 1 1 1 0 0 0]

[10, 5, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 w 0 w w 0 1]
[ 0 1 0 0 w 0 1 w w^2 0]
[ 0 0 1 0 0 0 1 w 0 w]
[ 0 0 0 1 w^2 0 1 0 1 w]
[ 0 0 0 0 0 1 1 1 w w^2]

[10, 6, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 w 0 w^2 0]
[ 0 1 0 0 0 0 0 1 w^2 w]
[ 0 0 1 0 0 0 1 1 0 1]
[ 0 0 0 1 0 0 0 w^2 w w^2]
[ 0 0 0 0 1 0 0 w^2 1 w]
[ 0 0 0 0 0 1 w w w^2 w]
_______________

n=11

[11, 4, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 1 w^2 0 w^2 1 0 1]
[ 0 1 0 0 0 1 0 w^2 w w 1]
[ 0 0 1 0 0 w^2 w^2 1 w^2 1 0]
[ 0 0 0 1 w w 1 w w 0 0]

[11, 5, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 w^2 0 w w^2 0 1]
[ 0 1 0 0 0 w^2 1 0 0 w^2 w^2]
[ 0 0 1 0 0 w w^2 0 w^2 w^2 0]
[ 0 0 0 1 0 0 1 w^2 w 1 0]
[ 0 0 0 0 1 w w w^2 w 0 0]

[11, 6, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 1 0 w^2 w^2 0]
[ 0 1 0 0 0 0 w 1 0 0 w^2]
[ 0 0 1 0 0 0 0 w^2 w 0 w^2]
[ 0 0 0 1 0 0 w^2 w^2 w^2 w w^2]
[ 0 0 0 0 1 0 w^2 w 0 w^2 0]
[ 0 0 0 0 0 1 0 0 1 1 1]

[11, 7, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 1 w w 0]
[ 0 1 0 0 0 0 0 w 0 0 w]
[ 0 0 1 0 0 0 0 w 0 0 w^2]
[ 0 0 0 1 0 0 0 w^2 0 w 0]
[ 0 0 0 0 1 0 0 w 0 w w]
[ 0 0 0 0 0 1 0 w 1 w^2 1]
[ 0 0 0 0 0 0 1 w w w^2 w]
_______________

n=12

[12, 4, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 w^2 w 0 0 1 1 1]
[ 0 1 0 0 w 0 1 w^2 w^2 w w w^2]
[ 0 0 1 0 1 w w^2 w^2 1 w w^2 0]
[ 0 0 0 1 w w 1 w w 0 0 0]

[12, 5, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 1 1 0 w w w 1]
[ 0 1 0 0 0 0 w 1 w w^2 w^2 w]
[ 0 0 1 0 0 w w^2 w w w^2 w 0]
[ 0 0 0 1 0 1 1 w 1 1 w 1]
[ 0 0 0 0 1 0 1 w w 1 0 w^2]

[12, 6, 4] Linear Code over GF(2^2)
[ 1 0 0 0 0 0 1 w 1 w 0 1]
[ 0 1 0 0 0 0 w 0 1 w^2 w^2 w^2]
[ 0 0 1 0 0 0 w^2 0 w^2 1 1 0]
[ 0 0 0 1 0 0 w w 1 0 0 0]
[ 0 0 0 0 1 0 w^2 w 0 w^2 0 0]
[ 0 0 0 0 0 1 0 0 1 1 1 0]

[12, 7, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 w^2 1 w 1]
[ 0 1 0 0 0 0 0 1 w^2 w w^2 w^2]
[ 0 0 1 0 0 0 0 1 w^2 w^2 w 0]
[ 0 0 0 1 0 0 0 1 w 0 w^2 0]
[ 0 0 0 0 1 0 0 w^2 1 w^2 0 0]
[ 0 0 0 0 0 1 0 w^2 0 w w^2 0]
[ 0 0 0 0 0 0 1 w w w^2 w 0]

[12, 8, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 w^2 w^2 0 w^2]
[ 0 1 0 0 0 0 0 0 w^2 w^2 w^2 1]
[ 0 0 1 0 0 0 0 0 w w^2 w w]
[ 0 0 0 1 0 0 0 0 1 w w^2 0]
[ 0 0 0 0 1 0 0 0 1 0 w^2 w]
[ 0 0 0 0 0 1 0 0 0 w 1 w^2]
[ 0 0 0 0 0 0 1 0 0 1 1 1]
[ 0 0 0 0 0 0 0 1 0 1 w w^2]
_______________

n=13

[13, 4, 8] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 1 1 w^2 1 1 w w^2 w 1]
[ 0 1 0 0 1 w 0 0 1 w^2 w w^2 1]
[ 0 0 1 0 1 w^2 w^2 w^2 0 w^2 w w 0]
[ 0 0 0 1 1 w 0 w w w w^2 0 w^2]

[13, 5, 7] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 1 0 w^2 w w^2 0 w^2 1]
[ 0 1 0 0 0 w w^2 w w w 1 w 1]
[ 0 0 1 0 0 w^2 0 1 w^2 w 1 w^2 0]
[ 0 0 0 1 0 w w^2 0 1 w^2 0 1 w^2]
[ 0 0 0 0 1 0 w^2 w w^2 1 w^2 1 0]

[13, 6, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 1 0 w w^2 1 w w]
[ 0 1 0 0 0 0 w^2 w 0 1 1 w^2 0]
[ 0 0 1 0 0 0 w^2 w^2 w^2 w w 0 w]
[ 0 0 0 1 0 0 0 w 0 1 w^2 1 w]
[ 0 0 0 0 1 0 w^2 w w^2 0 w^2 1 0]
[ 0 0 0 0 0 1 w^2 w w w^2 w^2 w w^2]

[13, 7, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 w 0 w^2 1 0 w 1]
[ 0 1 0 0 0 0 w^2 0 0 0 w w w]
[ 0 0 1 0 0 0 w 0 1 w^2 1 w 0]
[ 0 0 0 1 0 0 w 0 w 1 w^2 0 w]
[ 0 0 0 0 1 0 w 0 1 w w 0 w^2]
[ 0 0 0 0 0 1 0 0 w^2 0 1 w^2 w]
[ 0 0 0 0 0 0 0 1 0 w^2 w w^2 1]

[13, 8, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 w 0 1 w 0]
[ 0 1 0 0 0 0 0 0 w 0 w^2 w^2 1]
[ 0 0 1 0 0 0 0 0 1 1 w w^2 w]
[ 0 0 0 1 0 0 0 0 1 w w^2 1 1]
[ 0 0 0 0 1 0 0 0 w 1 w^2 0 1]
[ 0 0 0 0 0 1 0 0 0 w 1 w^2 1]
[ 0 0 0 0 0 0 1 0 w w^2 1 0 0]
[ 0 0 0 0 0 0 0 1 1 w 1 1 w^2]

**********************

Quaternary linear codes with five-dimensional hull (h=5)

n=10

[10, 5, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 1 0 w w 0]
[ 0 1 0 0 0 1 w 1 w^2 w]
[ 0 0 1 0 0 0 1 1 1 0]
[ 0 0 0 1 0 1 w w^2 1 w]
[ 0 0 0 0 1 0 0 1 1 1]
_______________

n=11

[11, 5, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 w^2 0 w w w^2 1]
[ 0 1 0 0 1 w 0 w w w 0]
[ 0 0 1 0 0 w 0 w w^2 w^2 1]
[ 0 0 0 1 1 w^2 0 w w^2 0 w]
[ 0 0 0 0 0 0 1 1 0 1 1]

[11, 6, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 w w w w 0]
[ 0 1 0 0 0 0 0 w w 0 w^2]
[ 0 0 1 0 0 0 1 w 0 w w^2]
[ 0 0 0 1 0 0 w w^2 w 0 w]
[ 0 0 0 0 1 0 w 0 1 1 w]
[ 0 0 0 0 0 1 w^2 w^2 w 0 w]
_______________

n=12

[12, 5, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 w w 1 0 1 w]
[ 0 1 0 0 0 w^2 w w 0 0 w^2 1]
[ 0 0 1 0 0 w w 0 0 w^2 w 1]
[ 0 0 0 1 0 w^2 1 0 w 0 w^2 w^2]
[ 0 0 0 0 1 w^2 w 1 0 1 w 0]

[12, 6, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 w 0 w^2 0 w^2 1 w^2 1]
[ 0 1 0 0 w 0 w 0 1 w w w]
[ 0 0 1 0 w 0 w 0 0 1 0 w]
[ 0 0 0 1 1 0 w 0 0 0 w^2 w]
[ 0 0 0 0 0 1 w^2 0 1 0 1 w]
[ 0 0 0 0 0 0 0 1 1 1 w w^2]

[12, 7, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 w 1 1 w^2]
[ 0 1 0 0 0 0 0 w w 0 w 1]
[ 0 0 1 0 0 0 0 1 0 w 0 w]
[ 0 0 0 1 0 0 0 1 w w^2 0 0]
[ 0 0 0 0 1 0 0 w w w 1 w]
[ 0 0 0 0 0 1 0 w w^2 0 w^2 0]
[ 0 0 0 0 0 0 1 0 0 w^2 1 w]
_______________

n=13

[13, 5, 6] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 1 1 1 1 1 1 1]
[ 0 1 0 0 0 w^2 w w 0 w w w^2 w^2]
[ 0 0 1 0 0 1 w^2 1 1 1 w^2 0 1]
[ 0 0 0 1 0 w^2 1 0 w^2 w w^2 w 1]
[ 0 0 0 0 1 w^2 1 w 0 0 w 1 0]

[13, 6, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 w^2 0 w 0 1 1 1 0]
[ 0 1 0 0 0 0 0 1 w w 0 1 0]
[ 0 0 1 0 0 w 0 w^2 w w^2 0 w 1]
[ 0 0 0 1 0 w^2 0 w^2 w w 1 0 w^2]
[ 0 0 0 0 1 w^2 0 w 0 w w 0 0]
[ 0 0 0 0 0 0 1 w w w^2 w 0 0]

[13, 7, 5] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 w^2 1 0 1 w]
[ 0 1 0 0 0 0 0 1 w w^2 1 w 0]
[ 0 0 1 0 0 0 0 1 1 0 w w 1]
[ 0 0 0 1 0 0 0 w w 1 w w 1]
[ 0 0 0 0 1 0 0 w^2 0 w^2 1 w^2 0]
[ 0 0 0 0 0 1 0 w w^2 w^2 1 0 1]
[ 0 0 0 0 0 0 1 w w^2 w w 1 w]

[13, 8, 4] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 0 w^2 w w^2 1]
[ 0 1 0 0 0 0 0 0 w 1 w w^2 0]
[ 0 0 1 0 0 0 0 0 w^2 0 w^2 0 1]
[ 0 0 0 1 0 0 0 0 1 0 w w^2 0]
[ 0 0 0 0 1 0 0 0 w^2 w^2 1 w w]
[ 0 0 0 0 0 1 0 0 w 0 w^2 w^2 w^2]
[ 0 0 0 0 0 0 1 0 w 1 w^2 w^2 1]
[ 0 0 0 0 0 0 0 1 w^2 w^2 0 1 0]

[13, 9, 3] Linear Code over GF(2^2)
Generator matrix:
[ 1 0 0 0 0 0 0 0 0 w^2 w w w]
[ 0 1 0 0 0 0 0 0 0 w^2 0 0 w^2]
[ 0 0 1 0 0 0 0 0 0 0 1 w 1]
[ 0 0 0 1 0 0 0 0 0 1 w w 1]
[ 0 0 0 0 1 0 0 0 0 w 0 w^2 w^2]
[ 0 0 0 0 0 1 0 0 0 0 w^2 w 1]
[ 0 0 0 0 0 0 1 0 0 w^2 1 w^2 0]
[ 0 0 0 0 0 0 0 1 0 1 w 0 0]
[ 0 0 0 0 0 0 0 0 1 w w w^2 w]