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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Stefka Bouyuklieva & Iliya Bouyukliev, 2024. "How to Find the Equivalence Classes in a Set of Linear Codes in Practice?," Mathematics, MDPI, vol. 12(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:328-:d:1322375
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