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A Class of Binary Codes Using a Specific Automorphism Group

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Bibliographic Details
Title: A Class of Binary Codes Using a Specific Automorphism Group
Authors: Driss Harzalla
Source: Mathematics ; Volume 12 ; Issue 24 ; Pages: 3962
Publisher Information: Multidisciplinary Digital Publishing Institute
Publication Year: 2024
Collection: MDPI Open Access Publishing
Subject Terms: binary linear code, self-orthogonal code, automorphism group, group actions, representation theory
Description: 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.
Document Type: text
File Description: application/pdf
Language: English
Relation: E: Applied Mathematics; https://dx.doi.org/10.3390/math12243962
DOI: 10.3390/math12243962
Availability: https://doi.org/10.3390/math12243962
Rights: https://creativecommons.org/licenses/by/4.0/
Accession Number: edsbas.EAAD1FC5
Database: BASE
Description
Abstract: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