An Extension of the Brouwer–Zimmermann Algorithm for Calculating the Minimum Weight of a Linear Code
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 dimension...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/19/2354 |
| _version_ | 1827680787170852864 |
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| author | Stefka Bouyuklieva Iliya Bouyukliev |
| author_facet | Stefka Bouyuklieva Iliya Bouyukliev |
| author_sort | Stefka Bouyuklieva |
| collection | DOAJ |
| description | 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 <span style="font-variant: small-caps;">QextNewEdition</span>. |
| first_indexed | 2024-03-10T06:56:28Z |
| format | Article |
| id | doaj.art-edd400138a95425ea80f28b96bc97ee7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T06:56:28Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-edd400138a95425ea80f28b96bc97ee72023-11-22T16:29:06ZengMDPI AGMathematics2227-73902021-09-01919235410.3390/math9192354An Extension of the Brouwer–Zimmermann Algorithm for Calculating the Minimum Weight of a Linear CodeStefka Bouyuklieva0Iliya Bouyukliev1Faculty of Mathematics and Informatics, St. Cyril and St. Methodius University of Veliko Tarnovo, 5000 Veliko Tarnovo, BulgariaInstitute of Mathematics and Informatics, Bulgarian Academy of Sciences, 5000 Veliko Tarnovo, BulgariaA 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 <span style="font-variant: small-caps;">QextNewEdition</span>.https://www.mdpi.com/2227-7390/9/19/2354linear codeHamming weightBrouwer–Zimmermann algorithm |
| spellingShingle | Stefka Bouyuklieva Iliya Bouyukliev An Extension of the Brouwer–Zimmermann Algorithm for Calculating the Minimum Weight of a Linear Code Mathematics linear code Hamming weight Brouwer–Zimmermann algorithm |
| title | An Extension of the Brouwer–Zimmermann Algorithm for Calculating the Minimum Weight of a Linear Code |
| title_full | An Extension of the Brouwer–Zimmermann Algorithm for Calculating the Minimum Weight of a Linear Code |
| title_fullStr | An Extension of the Brouwer–Zimmermann Algorithm for Calculating the Minimum Weight of a Linear Code |
| title_full_unstemmed | An Extension of the Brouwer–Zimmermann Algorithm for Calculating the Minimum Weight of a Linear Code |
| title_short | An Extension of the Brouwer–Zimmermann Algorithm for Calculating the Minimum Weight of a Linear Code |
| title_sort | extension of the brouwer zimmermann algorithm for calculating the minimum weight of a linear code |
| topic | linear code Hamming weight Brouwer–Zimmermann algorithm |
| url | https://www.mdpi.com/2227-7390/9/19/2354 |
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