Code4

Database for the paper “Shitao Li, Minjia Shi, San Ling, A mass formula for linear codes with prescribed hull dimension and related classification, IEEE Transactions on Information Theory, 2025, 71(1): 273-286.”

Table 1: Ternary linear codes with one-dimensional hull (h=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]

Table 1’: Optimal ternary linear codes with one-dimensional hull (h=1)

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

Table 2: Ternary 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]

Table 2’: Optimal ternary linear codes with two-dimensional hull (h=2)

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

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

[7, 3], [7, 4]
[8, 3], [8, 4], [8, 5]
[9, 3], [9, 4], [9, 5], [9, 6]

Table 3’: Optimal ternary linear codes with three-dimensional hull (h=3)

[7, 3, 3], [7, 4, 2]
[8, 3, 3], [8, 4, 3], [8, 5, 2]
[9, 3, 6], [9, 4, 5], [9, 5, 4], [9, 6, 3]