Original scientific paper

The cyclic codes of length $5p^s$ over $\mathbb{F}_{p^m}+u \mathbb{F}_{p^m}$ and their dual codes

Brahim Boudine orcid.org/0000-0003-1678-122X ; Department of Mathematics, Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar El Mahraz, Fez, Morocco
Jamal Laaouine orcid.org/0000-0002-8623-6094 ; Department of Mathematics, Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar El Mahraz, Fez, Morocco
Mohammed Elhassani Charkani ; Department of Mathematics, Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar El Mahraz, Fez, Morocco

Abstract

Let $p$ be a prime integer and $m$ be an integer such that $p \equiv 2\pmod 5$ or $p \equiv \pmod 5$ and $m$ is odd. We classify explicitly the cyclic codes of length $5p^s$ over $R= mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ with $u^2=0$ and we compute completely their dual codes.

Keywords

cyclic code, cyclotomic polynomial, error-correcting codes

Hrčak ID:

275700

URI

https://hrcak.srce.hr/275700

Publication date:

28.4.2022.

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