Minimal and maximal cyclic codes of length 2p

Heboub, Lakhdar; Mihoubi, Douadi

doi:10.47974/JDMSC-1569

Open Access Research Article

Minimal and maximal cyclic codes of length 2p

^*Lakhdar HeboubCorresponding authorlakhdar.heboub@univ-msila.dzDepartment of MathematicsLaboratory of Pure and Applied MathematicsM’sila UniversityM’sila, AlgeriaView full profile → , Douadi Mihoubidouadi.mihoubi@univ-msila.dzDepartment of MathematicsLaboratory of Pure and Applied MathematicsM’sila UniversityM’sila, AlgeriaView full profile →

* Corresponding author · click or hover a name for details

pp. 63–74Vol. 27Issue 1January 2024DOI: 10.47974/JDMSC-1569 Crossmark XML

Received:: 13 Jul 2021
Accepted:: 05 Jan 2022
Published Online:: 23 Jan 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1569
Pages:: 63–74

Abstract

In this paper, we compute the maximal and minimal codes of length 2p over finite fields Fq with p and q are distinct odd primes and f(p) = p – 1 is the multiplicative order of q modulo 2p. We show that, every cyclic code is a direct sum of minimal cyclic codes.

Keywords

Linear and cyclic codes Cyclotomic classes Decomposition of ideals in semi-simple algebras

Subject Classifications

[2010] 94B0594B1513A1594B6012E20

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