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

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, 2021, vol. 9, issue 19, 1-9

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 .

Keywords: linear code; Hamming weight; Brouwer–Zimmermann algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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