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Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances. (arXiv:2303.16729v1 [cs.IT])
March 30, 2023, 1:10 a.m. | Minjia Shi, Shitao Li, Tor Helleseth, Jon-Lark Kim
cs.CR updates on arXiv.org arxiv.org
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 $d_{so}(n,k)$ $(k
\le 6)$ …
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