On the construction of constacyclically permutable codes from constacyclic codes

Guanghui Zhang; Shuhua Liang; Guanghui Zhang; Shuhua Liang

doi:10.3934/math.2024628

AIMS Mathematics

2024, Volume 9, Issue 5: 12852-12869. doi: 10.3934/math.2024628

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Research article

On the construction of constacyclically permutable codes from constacyclic codes

Guanghui Zhang ¹,
Shuhua Liang ^{2
,
,}

1.
Department of Mathematics, Suqian University, Suqian, Jiangsu, 223800, China
2.
School of Economics and Management, Suqian University, Suqian, Jiangsu, 223800, China

Received: 28 February 2024 Revised: 25 March 2024 Accepted: 29 March 2024 Published: 03 April 2024
MSC : 94B15, 94B60

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.
- constacyclically permutable code,
- constacyclic code,
- primitive idempotent,
- group action
Citation: Guanghui Zhang, Shuhua Liang. On the construction of constacyclically permutable codes from constacyclic codes[J]. AIMS Mathematics, 2024, 9(5): 12852-12869. doi: 10.3934/math.2024628

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Abstract

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.

References

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