Hamming distance of repeated-root constacyclic codes of length \(2p^s\) over \({\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}\)

Abstract

Let p be an odd prime, and \(\delta\) be an arbitrary unit of the finite chain ring \({\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m} \,\, (u^2=0)\). The Hamming distances of all \(\delta\)-constacyclic codes of length \(2p^s\) over \({\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}\) are completely determined. We provide some examples from which some codes have better parameters than the existing ones. As applications, we determine all MDS repeated-root \(\delta\)-constacyclic codes of length \(2p^s\) over \(\mathbb F_{p^m}+u{\mathbb {F}}_{p^m}\).

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Acknowledgements

The authors would like to sincerely thank the referees and the editor for a very meticulous reading of this manuscript, and for valuable suggestions which help to create an improved final version.This paper is partially supported by the Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University.

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Correspondence to Manoj Kumar Singh.

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Dinh, H.Q., Gaur, A., Gupta, I. et al. Hamming distance of repeated-root constacyclic codes of length \(2p^s\) over \({\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}\). AAECC 31, 291–305 (2020). https://doi.org/10.1007/s00200-020-00432-0

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Keywords

  • Repeated-root codes
  • Constacyclic codes
  • Hamming distance
  • Finite chain rings