2024/06/22 by Sanjit Bhowmick, Bhowmick, Sanjit, Xiusheng Liu +1 · 1 citation
Computer Science · Engineering · Mathematics · #51E22 #94B05 #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2406.15794
openalex publication_date 2024/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study linear complementary pairs (LCP) of codes over finite non-commutative local rings. We further provide a necessary and sufficient condition for a pair of codes (C,D) to be LCP of codes over finite non-commutative Frobenius rings. The minimum distances d(C) and d(D^⊥) are defined as the security parameter for an LCP of codes (C, D). It was recently demonstrated that if C and D are both 2-sided LCP of group codes over a finite commutative Frobenius rings, D^⊥ and C are permutation equivalent in \citeLL23. As a result, the security parameter for a 2-sided group LCP (C, D) of codes is simply d(C). Towards this, we deliver an elementary proof of the fact that for a linear complementary pair of codes (C,D), where C and D are linear codes over finite non-commutative Frobenius rings, under certain conditions, the dual code D^⊥ is equivalent to C.