AIMS Mathematics (Apr 2024)

On the construction of constacyclically permutable codes from constacyclic codes

  • Guanghui Zhang ,
  • Shuhua Liang

DOI
https://doi.org/10.3934/math.2024628
Journal volume & issue
Vol. 9, no. 5
pp. 12852 – 12869

Abstract

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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.

Keywords