Skew Cyclic and Skew Constacyclic Codes over a Mixed Alphabet-Reference-Cited by-同舟云学术

Skew Cyclic and Skew Constacyclic Codes over a Mixed Alphabet

Published:2024-05-28 Issue:6 Volume:13 Page:360
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Gowdhaman Karthick¹,Mohan Cruz²^ORCID,Durairajan Chinnapillai³,Çalkavur Selda⁴,Solé Patrick⁵^ORCID

Affiliation:

1. Department of Mathematics, Presidency University, Bengaluru 560064, Karnataka, India

2. Department of Mathematics, Bishop Heber College, Bharathidasan University, Tiruchirapalli 620017, Tamil Nadu, India

3. Department of Mathematics, Bharathidasan University, Tiruchirapalli 620024, Tamil Nadu, India

4. Department of Mathematics, Faculty of Arts and Science, Kocaeli University, Kocaeli 41001, Turkey

5. I2M, Aix Marseille University, CNRS, 13009 Marseille, France

Abstract

In this note, we study skew cyclic and skew constacyclic codes over the mixed alphabet R=FqR1R2, where q=pm, p is an odd prime with m odd and R1=Fq+uFq with u2=u, and R2=Fq+uFq+vFq with u2=u,v2=v,uv=vu=0. Such codes consist of the juxtaposition of three codes of the same size over Fq,R1, and R2, respectively. We investigate the generator polynomial for skew cyclic codes over R. Furthermore, we discuss the structural properties of the skew cyclic and skew constacyclic codes over R. We also study their q-ary images under suitable Gray maps.

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/6/360/pdf

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