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arXiv · 2306.06903

Fuzzy linear codes based on nested linear codes

Jon-Lark Kim
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Abstract

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.

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Jon-Lark Kim. 2023-06-12. Fuzzy linear codes based on nested linear codes. https://doi.org/10.1016/j.fss.2023.108565

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