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A Class of Binary Codes Using a Specific Automorphism Group

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Název:	A Class of Binary Codes Using a Specific Automorphism Group
Autoři:	Driss Harzalla
Zdroj:	Mathematics ; Volume 12 ; Issue 24 ; Pages: 3962
Informace o vydavateli:	Multidisciplinary Digital Publishing Institute
Rok vydání:	2024
Sbírka:	MDPI Open Access Publishing
Témata:	binary linear code, self-orthogonal code, automorphism group, group actions, representation theory
Popis:	In this article, we showcase PSL(3,4) as the automorphism group for a specific class of three linear binary codes, C1, C2 and C3, with dimension 9. The demonstration involves leveraging the action of the group PSL(3,4), represented by invertible matrices of size 9 by 9 up to isomorphism, on the vector space F29. Additionally, we establish that these codes exhibit a three-weight self-orthogonal property. All computations presented in this paper were performed using the guava package of GAP (Groups, Algorithms, Programming) a system designed for computational discrete algebra.
Druh dokumentu:	text
Popis souboru:	application/pdf
Jazyk:	English
Relation:	E: Applied Mathematics; https://dx.doi.org/10.3390/math12243962
DOI:	10.3390/math12243962
Dostupnost:	https://doi.org/10.3390/math12243962
Rights:	https://creativecommons.org/licenses/by/4.0/
Přístupové číslo:	edsbas.EAAD1FC5
Databáze:	BASE

Popis
Abstrakt:	In this article, we showcase PSL(3,4) as the automorphism group for a specific class of three linear binary codes, C1, C2 and C3, with dimension 9. The demonstration involves leveraging the action of the group PSL(3,4), represented by invertible matrices of size 9 by 9 up to isomorphism, on the vector space F29. Additionally, we establish that these codes exhibit a three-weight self-orthogonal property. All computations presented in this paper were performed using the guava package of GAP (Groups, Algorithms, Programming) a system designed for computational discrete algebra.
DOI:	10.3390/math12243962