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.