Partial permutation decoding and PD-sets for Zps-linear generalized Hadamard codes

Mercè Villanueva, Adrián Torres-Martín

Research output: Contribution to journalArticleResearchpeer-review

Abstract

It is known that Zps-linear codes, which are the Gray map image of Zps-additive codes (linear codes over Zps), are systematic and a systematic encoding has been found. This makes Zps-linear codes suitable to apply the permutation decoding method. This technique is also based on the existence of r-PD-sets, which are subsets of the permutation automorphism group of the code. In this paper, we study the permutation automorphism group of Zps-linear generalized Hadamard codes of type (n;t1,…,ts) and show how to construct r-PD-sets of size r + 1, for all r up to an upper bound, in order to be able to perform a partial permutation decoding for these codes.
Original languageEnglish
Article number102316
Number of pages32
JournalFinite Fields and Their Applications
Volume93
DOIs
Publication statusPublished - Jan 2024

Keywords

  • Permutation decoding
  • PD-set
  • Automorphism group
  • Generalized Hadamard code
  • Zps-linear code
  • Gray map

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