Additive codes attaining the Griesmer bound
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913099763679232 |
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| author | Kurz, Sascha |
| author_facet | Kurz, Sascha |
| contents | Additive codes may have better parameters than linear codes. However, still very few cases are known and the explicit construction of such codes is a challenging problem. Here we show that a Griesmer type bound for the length of additive codes can always be attained with equality if the minimum distance is sufficiently large. This solves the problem for the optimal parameters of additive codes when the minimum distance is large and yields many infinite series of additive codes that outperform linear codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14615 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Additive codes attaining the Griesmer bound Kurz, Sascha Information Theory Combinatorics 05B25, 94B65, 94B60 Additive codes may have better parameters than linear codes. However, still very few cases are known and the explicit construction of such codes is a challenging problem. Here we show that a Griesmer type bound for the length of additive codes can always be attained with equality if the minimum distance is sufficiently large. This solves the problem for the optimal parameters of additive codes when the minimum distance is large and yields many infinite series of additive codes that outperform linear codes. |
| title | Additive codes attaining the Griesmer bound |
| topic | Information Theory Combinatorics 05B25, 94B65, 94B60 |
| url | https://arxiv.org/abs/2412.14615 |