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Repeated-Root Constacyclic Codes of Length \(k\ell p^s\)

  • Yan Liu
  • Minjia ShiEmail author
Article
  • 2 Downloads

Abstract

In this paper, we investigate all repeated-root constacyclic codes and their duals of length \(k\ell p^s\) over \({\mathbb {F}}_q\) in terms of generator polynomials, where \(\ell \) is an odd prime different from p and k is an odd prime different from both \(\ell \) and p such that \(k=4h+1\) for some prime h. As an application, the characterization and enumeration of all self-dual repeated-root cyclic codes of length \(2^sk\ell \) over \({\mathbb {F}}_q\) are obtained.

Keywords

Constacyclic code Dual code Generator polynomial Self-dual repeated-root cyclic code 

Mathematics Subject Classification

94B25 05E30 

Notes

Acknowledgements

This research is supported by National Natural Science Foundation of China (61672036) and Excellent Youth Foundation of Natural Science Foundation of Anhui Province (No. 1808085J20).

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesAnhui UniversityHefeiChina

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