On the construction of constacyclically permutable codes from constacyclic codes

On the construction of constacyclically permutable codes from constacyclic codes

In this paper, we propose a way to partition any constacyclic code over a finite field in its equivalence classes according to the algebraic structure of the code. Such a method gives the generalization of cyclically permutable codes (CPCs), which are called constacyclically permutable codes (CCPCs)...

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Bibliographic Details
Published in:AIMS mathematics Vol. 9; no. 5; pp. 12852 - 12869
Main Authors: Zhang, Guanghui, Liang, Shuhua
Format: Journal Article
Language:English
Published: AIMS Press 01-01-2024
Subjects:
constacyclic code
constacyclically permutable code
group action
primitive idempotent
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Summary:In this paper, we propose a way to partition any constacyclic code over a finite field in its equivalence classes according to the algebraic structure of the code. Such a method gives the generalization of cyclically permutable codes (CPCs), which are called constacyclically permutable codes (CCPCs), and it is useful to derive a CCPC from a given constacyclic code. Moreover, we present an enumerative formula for the code size of such a CCPC, with all of the terms being positive integers, and we provide an algebraic method to produce such a CCPC.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024628