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On LCP codes over a mixed ring alphabet (2309.14217v1)
Published 25 Sep 2023 in cs.IT, math.IT, and math.RA
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.