AHU-coding

Database for the paper “Shitao Li, Minjia Shi, Characterization and classification of binary linear codes with various hull dimensions from an improved mass formula, IEEE Transactions on Information Theory, 2024, 70(5): 3357-3372.”

Table 1: Binary linear codes with one-dimensional hull (h=1)

[2, 1]
[3, 1], [3, 2]
[4, 1], [4, 2], [4, 3]
[5, 1], [5, 2], [5, 3], [5, 4]
[6, 1], [6, 2], [6, 3], [6, 4], [6, 5]
[7, 1], [7, 2], [7, 3], [7, 4], [7, 5], [7, 6]
[8, 1], [8, 2], [8, 3], [8, 4], [8, 5], [8, 6], [8, 7]
[9, 1], [9, 2], [9, 3], [9, 4], [9, 5], [9, 6], [9, 7], [9, 8]
[10, 1], [10, 2], [10, 3], [10, 4], [10, 5], [10, 6], [10, 7], [10, 8], [10, 9]
[11, 1], [11, 2], [11, 3], [11, 4], [11, 5], [11, 6], [11, 7], [11, 8], [11, 9], [11, 10]
[12, 1], [12, 2], [12, 3], [12, 4], [12, 5], [12, 6], [12, 7], [12, 8], [12, 9], [12, 10], [12, 11]

Table 2: Optimal binary linear codes with one-dimensional hull (h=1)

[2, 1, 2]
[3, 1, 2], [3, 2, 1]
[4, 1, 4], [4, 2, 1], [4, 3, 2]
[5, 1, 4], [5, 2, 3], [5, 3, 2], [5, 4, 1]
[6, 1, 6], [6, 2, 3], [6, 3, 2], [6, 4, 1], [6, 5, 2]
[7, 1, 6], [7, 2, 4], [7, 3, 3], [7, 4, 2], [7, 5, 2], [7, 6, 1]
[8, 1, 8], [8, 2, 4], [8, 3, 4], [8, 4, 3], [8, 5, 2], [8, 6, 1], [8, 7, 2]
[9, 1, 8], [9, 2, 5], [9, 3, 4], [9, 4, 3], [9, 5, 3], [9, 6, 2], [9, 7, 2], [9, 8, 1]
[10, 1, 10], [10, 2, 5], [10, 3, 5], [10, 4, 4], [10, 5, 3], [10, 6, 3], [10, 7, 2], [10, 8, 1], [10, 9, 2]
[11, 1, 10], [11, 2, 7], [11, 3, 6], [11, 4, 5], [11, 5, 4], [11, 6, 3], [11, 7, 3], [11, 8, 2], [11, 9, 2], [11, 10, 1]
[12, 1, 12], [12, 2, 7], [12, 3, 6], [12, 4, 5], [12, 5, 4], [12, 6, 4], [12, 7, 4], [12, 8, 3], [12, 9, 2], [12, 10, 1], [12, 11, 2]
[13, 1, 12], [13, 2, 8], [13, 3, 6], [13, 4, 6], [13, 5, 5], [13, 6, 4], [13, 7, 4], [13, 8, 3], [13, 9, 2], [13, 10, 2], [13, 11, 2], [13, 12, 1]

Table 3: Binary linear codes with two-dimensional hull (h=2)

[4, 2]
[5, 2], [5, 3]
[6, 2], [6, 3], [6, 4]
[7, 2], [7, 3], [7, 4], [7, 5]
[8, 2], [8, 3], [8, 4], [8, 5], [8, 6]
[9, 2], [9, 3], [9, 4], [9, 5], [9, 6], [9, 7]
[10, 2], [10, 3], [10, 4], [10, 5], [10, 6], [10, 7], [10, 8]
[11, 2], [11, 3], [11, 4], [11, 5], [11, 6], [11, 7], [11, 8], [11, 9]
[12, 2], [12, 3], [12, 4], [12, 5], [12, 6], [12, 7], [12, 8], [12, 9], [12, 10]

Table 4: Optimal binary linear codes with two-dimensional hull (h=2)

[4, 2, 2]
[5, 2, 2], [5, 3, 1]
[6, 2, 4], [6, 3, 3], [6, 4, 2]
[7, 2, 4], [7, 3, 3], [7, 4, 2], [7, 5, 1]
[8, 2, 4], [8, 3, 4], [8, 4, 3], [8, 5, 2], [8, 6, 2]
[9, 2, 4], [9, 3, 4], [9, 4, 4], [9, 5, 3], [9, 6, 2], [9, 7, 1]
[10, 2, 6], [10, 3, 4], [10, 4, 4], [10, 5, 3], [10, 6, 3], [10, 7, 2], [10, 8, 2]
[11, 2, 6], [11, 3, 5], [11, 4, 4], [11, 5, 4], [11, 6, 4], [11, 7, 3], [11, 8, 2], [11, 9, 1]
[12, 2, 8], [12, 3, 5], [12, 4, 6], [12, 5, 4], [12, 6, 4], [12, 7, 3], [12, 8, 3], [12, 9, 2], [12, 10, 2]
[13, 2, 8], [13, 3, 7], [13, 4, 6], [13, 5, 5], [13, 6, 4], [13, 7, 4], [13, 8, 4], [13, 9, 3], [13, 10, 2], [13, 11, 1]

Table 5: Binary linear codes with three-dimensional hull (h=3)

[6, 3]
[7, 3], [7, 4]
[8, 3], [8, 4], [8, 5]
[9, 3], [9, 4], [9, 5], [9, 6]
[10, 3], [10, 4], [10, 5], [10, 6], [10, 7]
[11, 3], [11, 4], [11, 5], [11, 6], [11, 7], [11, 8]
[12, 3], [12, 4], [12, 5], [12, 6], [12, 7], [12, 8], [12, 9]

Table 6: Optimal binary linear codes with three-dimensional hull (h=3)

[6, 3, 2]
[7, 3, 4], [7, 4, 3]
[8, 3, 4], [8, 4, 3], [8, 5, 2]
[9, 3, 4], [9, 4, 4], [9, 5, 3], [9, 6, 2]
[10, 3, 4], [10, 4, 4], [10, 5, 4], [10, 6, 2], [10, 7, 2]
[11, 3, 4], [11, 4, 4], [11, 5, 4], [11, 6, 3], [11, 7, 2], [11, 8, 2]
[12, 3, 6], [12, 4, 4], [12, 5, 4], [12, 6, 4], [12, 7, 4], [12, 8, 2], [12, 9, 2]
[13, 3, 6], [13, 4, 5], [13, 5, 4], [13, 6, 4], [13, 7, 4], [13, 8, 3], [13, 9, 2], [13, 10, 2]

Table 7: Binary linear codes with four-dimensional hull (h=4)

[8, 4]
[9, 4], [9, 5]
[10, 4], [10, 5], [10, 6]
[11, 4], [11, 5], [11, 6], [11, 7]
[12, 4], [12, 5], [12, 6], [12, 7], [12, 8]

Table 8: Optimal binary linear codes with four-dimensional hull (h=4)

[8, 4, 4]
[9, 4, 4], [9, 5, 2]
[10, 4, 4], [10, 5, 4], [10, 6, 2]
[11, 4, 4], [11, 5, 4], [11, 6, 3], [11, 7, 2]
[12, 4, 4], [12, 5, 4], [12, 6, 4], [12, 7, 3], [12, 8, 2]
[13, 4, 4], [13, 5, 4], [13, 6, 4], [13, 7, 4], [13, 8, 3], [13, 9, 2]

Table 9: Binary linear codes with five-dimensional hull (h=5)

[10, 5]
[11, 5], [11, 6]
[12, 5], [12, 6], [12, 7]
[13, 5], [13, 6], [13, 7], [13, 8]

Table 10: Optimal binary linear codes with five-dimensional hull (h=5)

[10, 5, 2]
[11, 5, 4], [11, 6, 3]
[12, 5, 4], [12, 6, 3], [12, 7, 3]
[13, 5, 4], [13, 6, 4], [13, 7, 4], [13, 8, 2]

Table 11: Binary linear codes with six-dimensional hull (h=6)

[12, 6]
[13, 6], [13, 7]

Table 12: Optimal binary linear codes with six-dimensional hull (h=6)

[12, 6, 4]
[13, 6, 4], [13, 7, 3]