How to Find the Equivalence Classes in a Set of Linear Codes in Practice?

Stefka Bouyuklieva () and Iliya Bouyukliev
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Stefka Bouyuklieva: Faculty of Mathematics and Informatics, St. Cyril and St. Methodius University of Veliko Tarnovo, 5000 Veliko Tarnovo, Bulgaria
Iliya Bouyukliev: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 5000 Veliko Tarnovo, Bulgaria

Mathematics, 2024, vol. 12, issue 2, 1-14

Abstract: An algorithm for equivalence of linear codes over finite fields is presented. Its main advantage is that it can extract exactly one representative from each equivalence class among a large number of linear codes. It can also be used as a test for isomorphism of binary matrices. The algorithm is implemented in the program LCequivalence , which is designed to obtain the inequivalent codes in a set of linear codes over a finite field with q < 64 elements. This program is a module of the free software package QextNewEdition for constructing, classifying and studying linear codes.

Keywords: linear code; code equivalence; canonical form; graph isomorphism problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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