On LCP codes over a mixed ring alphabet
Information Theory
2023-09-26 v1 math.IT
Rings and Algebras
Abstract
In this paper, we introduce a standard generator matrix for mixed-alphabet linear codes over finite chain rings. Furthermore, we show that, when one has a linear complementary pair (LCP) of mixed-alphabet linear codes, both codes are weakly-free. Additionally, we establish that any mixed-alphabet product group code is separable. Thus, if one has a pair of mixed-alphabet product group codes over a finite chain ring that forms a LCP, it follows that and the Euclidean dual of are permutation equivalent.
Keywords
Cite
@article{arxiv.2309.14217,
title = {On LCP codes over a mixed ring alphabet},
author = {Maryam Bajalan and Javier de la Cruz and Alexandre Fotue-Tabue and Edgar Martínez-Moro},
journal= {arXiv preprint arXiv:2309.14217},
year = {2023}
}
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Submitted to Discrete Mathematics