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A Class of Binary Codes Using a Specific Automorphism Group

Author

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  • Driss Harzalla

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

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.

Suggested Citation

  • Driss Harzalla, 2024. "A Class of Binary Codes Using a Specific Automorphism Group," Mathematics, MDPI, vol. 12(24), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3962-:d:1545576
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