Some Results on Images of a Class of λ-Constacyclic Codes Over Finite Fields

Jian Gao,Juan Li,Yongkang Wang

doi:10.1109/access.2020.2982909

Abstract

In this paper, we show that any λ-constacyclic code over F qm is a λ-constacyclic code over F q under some special maps. Moreover, we show that the images of these λ_constacyclic codes can be put into the concatenated form.

Highlights

Cyclic codes are one of the most interesting families of codes because of their good algebraic structures. λ-Constacyclic codes were introduced as an extension of the class of cyclic codes and form an important class of linear codes in coding theory [2], [4]
We identify C with f (C), i.e. the λ-constacyclic code C of length n over Fq is an ideal of Fq[x]/ xn − λ
In this paper, we studied some results on the images of a class of constacyclic codes over finite fields

Summary

INTRODUCTION

Cyclic codes are one of the most interesting families of codes because of their good algebraic structures. λ-Constacyclic codes were introduced as an extension of the class of cyclic codes and form an important class of linear codes in coding theory [2], [4]. Λ-Constacyclic codes were introduced as an extension of the class of cyclic codes and form an important class of linear codes in coding theory [2], [4] These codes have practical applications such as mathematics and engineering. One interesting research problem of cyclic codes in coding theory is that the q-image of this class of liner codes over finite fields. The q-image of cyclic codes over finite fields can be used to construct good linear codes with long length. Similar to the problem for cyclic codes over the finite field Fqm , in this paper, we discuss the q-images of λ-constacyclic codes over Fqm. Further, we give the description on q-images of λ-constacyclic codes in a concatenated form.

PRELIMINARIES

THE PRIMARY COMPONENTS OF λ-CONSTACYCLIC CODES

THE NONTRIVIAL PRIMARY COMPONENT

CONCLUSION