Fuzzy linear codes based on nested linear codes
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912018335793152 |
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| author | Kim, Jon-Lark |
| author_facet | Kim, Jon-Lark |
| contents | In this paper, we describe a correspondence between a fuzzy linear code and a family of nested linear codes. We also describe the arithmetic of fuzzy linear codes. As a special class of nested linear codes, we consider a family of nested self-orthogonal codes. A linear code is self-orthogonal if it is contained in its dual and self-dual if it is equal to its dual. We introduce a definition of fuzzy self-dual or self-orthogonal codes which include classical self-dual or self-orthogonal codes. As examples, we construct several interesting classes of fuzzy linear codes including fuzzy Hamming codes, fuzzy Golay codes, and fuzzy Reed-Muller codes. We also give a general decoding algorithm for fuzzy linear codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_06903 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fuzzy linear codes based on nested linear codes Kim, Jon-Lark Information Theory 03E72, 94B05 In this paper, we describe a correspondence between a fuzzy linear code and a family of nested linear codes. We also describe the arithmetic of fuzzy linear codes. As a special class of nested linear codes, we consider a family of nested self-orthogonal codes. A linear code is self-orthogonal if it is contained in its dual and self-dual if it is equal to its dual. We introduce a definition of fuzzy self-dual or self-orthogonal codes which include classical self-dual or self-orthogonal codes. As examples, we construct several interesting classes of fuzzy linear codes including fuzzy Hamming codes, fuzzy Golay codes, and fuzzy Reed-Muller codes. We also give a general decoding algorithm for fuzzy linear codes. |
| title | Fuzzy linear codes based on nested linear codes |
| topic | Information Theory 03E72, 94B05 |
| url | https://arxiv.org/abs/2306.06903 |