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An Extension of the Brouwer–Zimmermann Algorithm for Calculating the Minimum Weight of a Linear Code

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

A modification of the Brouwer–Zimmermann algorithm for calculating the minimum weight of a linear code over a finite field is presented. The aim was to reduce the number of codewords for consideration. The reduction is significant in cases where the length of a code is not divisible by its dimensions. The proposed algorithm can also be used to find all codewords of weight less than a given constant. The algorithm is implemented in the software package QextNewEdition .

Suggested Citation

  • Stefka Bouyuklieva & Iliya Bouyukliev, 2021. "An Extension of the Brouwer–Zimmermann Algorithm for Calculating the Minimum Weight of a Linear Code," Mathematics, MDPI, vol. 9(19), pages 1-9, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2354-:d:640801
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