Embedding in MDS codes and Latin cubes
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866914762198089728 |
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| author | Potapov, Vladimir N. |
| author_facet | Potapov, Vladimir N. |
| contents | An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance $ρ$ and length $d$ can be embedded into an MDS code with the same code distance and length but under a larger alphabet. As a corollary we obtain embeddings of systems of partial mutually orthogonal Latin cubes and $n$-ary quasigroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_14962 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Embedding in MDS codes and Latin cubes Potapov, Vladimir N. Combinatorics 05B15 An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance $ρ$ and length $d$ can be embedded into an MDS code with the same code distance and length but under a larger alphabet. As a corollary we obtain embeddings of systems of partial mutually orthogonal Latin cubes and $n$-ary quasigroups. |
| title | Embedding in MDS codes and Latin cubes |
| topic | Combinatorics 05B15 |
| url | https://arxiv.org/abs/2109.14962 |