Code distances: a new family of invariants of linear codes
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908549074911232 |
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| author | Camps-Moreno, Eduardo Gorla, Elisa López, Hiram H. |
| author_facet | Camps-Moreno, Eduardo Gorla, Elisa López, Hiram H. |
| contents | In this paper, we introduce code distances, a new family of invariants for linear codes. We establish some properties and prove bounds on the code distances, and show that they are not invariants of the matroid (for a linear block code) or $q$-polymatroid (for a rank-metric code) associated to the code. By means of examples, we show that the code distances allow us to distinguish some inequivalent MDS or MRD codes with the same parameters. We also show that no duality holds, i.e., the sequence of code distances of a code does not determine the sequence of code distances of its dual. Further, we define a greedy and an asymptotic version of code distances. Finally, we relate these invariants to other invariants of linear codes, such as the maximality degree, the covering radius, and the partial distances of polar codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16424 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Code distances: a new family of invariants of linear codes Camps-Moreno, Eduardo Gorla, Elisa López, Hiram H. Information Theory In this paper, we introduce code distances, a new family of invariants for linear codes. We establish some properties and prove bounds on the code distances, and show that they are not invariants of the matroid (for a linear block code) or $q$-polymatroid (for a rank-metric code) associated to the code. By means of examples, we show that the code distances allow us to distinguish some inequivalent MDS or MRD codes with the same parameters. We also show that no duality holds, i.e., the sequence of code distances of a code does not determine the sequence of code distances of its dual. Further, we define a greedy and an asymptotic version of code distances. Finally, we relate these invariants to other invariants of linear codes, such as the maximality degree, the covering radius, and the partial distances of polar codes. |
| title | Code distances: a new family of invariants of linear codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2509.16424 |