On The Classification of Some Three Dimensional Quaternary Optimal Self-orthogonal Codes

摘要

The classification of quaternary [21s + t, 3, d] codes with d ≥ 16s and without zero coordinates is reduced to the classification of quaternary [21c(3, s, t) + t, k, d] code for s ≥ 1 and 0 ≤ t ≤ 20, where c(3, s, t) ≤ min{s,3t} is a function of 3, s, and t. Quaternary optimal Hermitian self-orthogonal codes are characterized by systems of linear equations. Based on these two results, the complete classification of [21s + t, 3] optimal self-orthogonal codes with s ≥ 1 and t ∈ {9,11} is obtained, and the generator matrices and weight polynomials of these 3-dimensional optimal self-orthogonal codes are also given. All these codes meeting the Griesmer bound.