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- W4306178148 abstract "The purpose of this paper is to solve the two conjectures on the largest minimum distance $d_{so}(n,5)$ of a binary self-orthogonal $[n,5]$ code proposed by Kim and Choi (IEEE Trans. Inf. Theory, 2022). The determination of $d_{so}(n,k)$ has been a fundamental and difficult problem in coding theory because there are too many binary self-orthogonal codes as the dimension $k$ increases. Recently, Kim et al. (2021) considered the shortest self-orthogonal embedding of a binary linear code, and many binary optimal self-orthogonal $[n,k]$ codes were constructed for $k=4,5$. Kim and Choi (2022) improved some results of Kim et al. (2021) and made two conjectures on $d_{so}(n,5)$. In this paper, we develop a general method to determine the exact value of $d_{so}(n,k)$ for $k=5,6$ and show that the two conjectures made by Kim and Choi (2022) are true." @default.
- W4306178148 created "2022-10-14" @default.
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- W4306178148 date "2022-10-12" @default.
- W4306178148 modified "2023-10-16" @default.
- W4306178148 title "Two conjectures on the largest minimum distances of binary self-orthogonal codes with dimension 5" @default.
- W4306178148 doi "https://doi.org/10.48550/arxiv.2210.06241" @default.
- W4306178148 hasPublicationYear "2022" @default.
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