$\Theta_S-$cyclic codes over $A_k$
Irwansyah, Aleams Barra, Steven T. Dougherty, Ahmad Muchlis, Intan, Muchtadi-Alamsyah, Patrick Sol\'e, Djoko Suprijanto, and Olfa Yemen
TL;DR
This paper investigates a class of cyclic codes over specific rings, characterizes their structure via binary images, explores duality properties with Hermitian inner-products, and provides methods for constructing such codes.
Contribution
It introduces a new class of $ heta_S$-cyclic codes over $A_k$, characterizes their properties, and offers construction techniques, expanding the understanding of cyclic codes over rings.
Findings
$ heta_S$-cyclic codes are characterized by their binary images.
The Hermitian dual of a $ heta_S$-cyclic code is also $ heta_S$-cyclic.
Construction methods for $ heta_S$-cyclic codes are provided.
Abstract
We study cyclic codes over the family of rings We characterize cyclic codes in terms of their binary images. A family of Hermitian inner-products is defined and we prove that if a code is cyclic then its Hermitian dual is also cyclic. Finally, we give constructions of cyclic codes.
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · graph theory and CDMA systems