On The Classification of Binary Optimal Self-Orthogonal Codes

The classification of binary [n,k,d] codes with d ges s2k-1 and without zero coordinates is reduced to the classification of binary [(2k-1)c (k,s,t)+t,k,d] code for n =(2k-1)s+t, s ges 1 and 1 les t les 2k-2, where c(k,s,t) les min{s, t} is a function of k, s, and t. Binary [15s +t, 4] optimal self-orthogonal codes are characterized by systems of linear equations. Based on these two results, the complete classification of [15s +t,4] optimal self-orthogonal codes for t isin {1,2,6,7,8,9,13,14} and s ges 1 is obtained, and the generator matrices and weight polynomials of these 4-dimensional optimal self-orthogonal codes are also given.