On the classification of binary optimal self-orthogonal codes

The classification of binary [n,k,d] codes with d ≥s2^k-1 and without zero coordinates is reduced to the classification of binary [(2^k-1)c(k,s,t) + t,k,d] code for n=(2^k-1)s + t, s ≥ 1 and 1 ≤ t ≤ 2^k-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 for t ∈ {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.