Linear Complementary Pair Of Group Codes over Finite Chain Rings

TL;DR

This paper extends the study of linear complementary pairs of group codes from finite fields to finite chain rings, analyzing their properties and security parameters in this broader algebraic context.

Contribution

It generalizes known results about 2-sided group codes over finite fields to the setting of finite chain rings, providing new insights into their structure and security.

Findings

Extended the equivalence of 2-sided group codes over finite fields to finite chain rings.

Characterized the security parameter for LCPs over finite chain rings.

Provided theoretical foundations for cryptographic applications over chain rings.

Abstract

Linear complementary dual (LCD) codes and linear complementary pair (LCP) of codes over finite fields have been intensively studied recently due to their applications in cryptography, in the context of side-channel and fault injection attacks. The security parameter for an LCP of codes $(C,D)$ is defined as the minimum of the minimum distances $d(C)$ and $d(D^\bot)$. It has been recently shown that if $C$ and $D$ are both 2-sided group codes over a finite field, then $C$ and $D^\bot$ are permutation equivalent. Hence the security parameter for an LCP of 2-sided group codes $(C,D)$ is simply $d(C)$. We extend this result to 2-sided group codes over finite chain rings.