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arXiv · 2309.14217

On LCP codes over a mixed ring alphabet

Maryam Bajalan·Javier de la Cruz·Alexandre Fotue-Tabue·Edgar Martínez-Moro
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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 $\{C, D\}$ of mixed-alphabet product group codes over a finite chain ring that forms a LCP, it follows that $C$ and the Euclidean dual of $D$ are permutation equivalent.

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Maryam Bajalan, Javier de la Cruz, Alexandre Fotue-Tabue, Edgar Martínez-Moro. 2023-09-25. On LCP codes over a mixed ring alphabet. https://arxiv.org/abs/2309.14217

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