On LCP codes over a mixed ring alphabet
Maryam Bajalan, Javier de la Cruz, Alexandre Fotue-Tabue, Edgar, Mart\'inez-Moro

TL;DR
This paper studies linear codes over mixed finite chain rings, introducing a generator matrix, analyzing LCP properties, and establishing separability and permutation equivalence of certain code pairs.
Contribution
It provides a standard generator matrix for mixed-alphabet codes and proves new properties of LCP and product group codes over finite chain rings.
Findings
LCP codes over mixed rings are weakly-free.
Mixed-alphabet product group codes are separable.
LCP pairs imply permutation equivalence of codes and duals.
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.
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Taxonomy
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding · graph theory and CDMA systems
