Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances
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The purpose of this paper is two-fold. First, we characterize the existence of binary self-orthogonal codes meeting the Griesmer bound by employing Solomon-Stiffler codes and some related residual codes. Second, using such a characterization, we determine the exact value of d_so(n,7) except for five special cases and the exact value of d_so(n,8) except for 41 special cases, where d_so(n,k) denotes the largest minimum distance among all binary self-orthogonal [n, k] codes. Currently, the exact value of d_so(n,k) (k ≤ 6) was determined by Shi et al. (2022). In addition, we develop a general method to prove the nonexistence of some binary self-orthogonal codes by considering the residual code of a binary self-orthogonal code.
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