On linear lexicographic codes: Ninth column construction of the ternary Golay code
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917292006178816 |
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| author | Irie, Yuki |
| author_facet | Irie, Yuki |
| contents | We characterize linear lexicographic $p$-ary codes. Using this characterization, when $p \ge 3$, we determine the dimensions of linear lexicographic codes obtained from several bases including the standard basis, except for those of certain minimum distances. In these excluded cases, we may obtain linear codes of higher dimensions; for instance, when $p = 3$ and $d = 6$, the ternary Golay code is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21067 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On linear lexicographic codes: Ninth column construction of the ternary Golay code Irie, Yuki Combinatorics 94B05 We characterize linear lexicographic $p$-ary codes. Using this characterization, when $p \ge 3$, we determine the dimensions of linear lexicographic codes obtained from several bases including the standard basis, except for those of certain minimum distances. In these excluded cases, we may obtain linear codes of higher dimensions; for instance, when $p = 3$ and $d = 6$, the ternary Golay code is obtained. |
| title | On linear lexicographic codes: Ninth column construction of the ternary Golay code |
| topic | Combinatorics 94B05 |
| url | https://arxiv.org/abs/2602.21067 |