Fuzzy linear codes based on nested linear codes
Information Theory
2024-09-10 v2 math.IT
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.
Keywords
Cite
@article{arxiv.2306.06903,
title = {Fuzzy linear codes based on nested linear codes},
author = {Jon-Lark Kim},
journal= {arXiv preprint arXiv:2306.06903},
year = {2024}
}