On The Classification of Binary Optimal Self-Orthogonal Codes.

The classification of binary [n, k, d] codes with d ⩾ 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 =(k - 1)s + t, s ⩾ 1 and 1 ⩽ t ⩽ - 2k - 2, where c(k, s, t) ⩽ 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 fort t Є {1,2,6,7,8,9,13,14} and s ⩾ 1 is obtained, and the generator matrices and weight polynomials of these 4-dimensional optimal self-orthogonal codes are also given. [ABSTRACT FROM AUTHOR]