A Generalization of Cyclic Code Equivalence Algorithm to Constacyclic Codes

TL;DR

This paper extends an efficient cyclic code equivalence algorithm to constacyclic codes, enabling the discovery of new codes with improved parameters, including 23 codes surpassing previous minimum distances.

Contribution

The paper introduces a generalized algorithm for constacyclic code equivalence testing, facilitating the identification of better-performing codes.

Findings

Found 23 new codes with improved minimum distances

Extended the equivalence algorithm from cyclic to constacyclic codes

Demonstrated the algorithm's effectiveness in discovering codes with good parameters

Abstract

Recently, a new algorithm to test equivalence of two cyclic codes has been introduced which is efficient and produced useful results. In this work, we generalize this algorithm to constacyclic codes. As an application of the algorithm we found many constacyclic codes with good parameters and properties. In particular, we found 23 new codes that improve the minimum distances of BKLCs.