A Class of Binary Codes Using a Specific Automorphism Group

Driss Harzalla ()
Additional contact information
Driss Harzalla: National School of Applied Sciences ENSAS, Cadi Ayyad University, Route Sidi Bouzid BP 63 Rue Sidi M’Barek, Safi 46000, Morocco

Mathematics, 2024, vol. 12, issue 24, 1-10

Abstract: In this article, we showcase P S L ( 3 , 4 ) as the automorphism group for a specific class of three linear binary codes, C 1 , C 2 and C 3 , with dimension 9. The demonstration involves leveraging the action of the group P S L ( 3 , 4 ) , represented by invertible matrices of size 9 by 9 up to isomorphism, on the vector space F 2 9 . 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.

Keywords: binary linear code; self-orthogonal code; automorphism group; group actions; representation theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/24/3962/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/24/3962/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:24:p:3962-:d:1545576

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().