Classification of Quaternary [21s+1,3] Optimal Self-orthogonal Codes

Abstract

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+1,3] optimal self-orthogonal codes for s≥1 is obtained, and the generator matrices and weight polynomials of these 3-dimensional optimal self-orthogonal codes are also given.