Linear Binary Codes Correcting One or More Errors
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909960508538880 |
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| author | Izhitskii, Timofei |
| author_facet | Izhitskii, Timofei |
| contents | This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal codeword length is derived. For the general case, a simple lower bound for the parameters of linear codes is derived from an analysis of the coset structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12591 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear Binary Codes Correcting One or More Errors Izhitskii, Timofei Information Theory 94B25 (Primary), 94B05, 94B65 (Secondary) This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal codeword length is derived. For the general case, a simple lower bound for the parameters of linear codes is derived from an analysis of the coset structure. |
| title | Linear Binary Codes Correcting One or More Errors |
| topic | Information Theory 94B25 (Primary), 94B05, 94B65 (Secondary) |
| url | https://arxiv.org/abs/2512.12591 |