Systematic encoding for Z2s-linear codes

Adrian Torres-Martin, Merce Villanueva

Research output: Chapter in BookChapterResearchpeer-review

Abstract

The {\mathbb{Z}_{{2^s}}}-additive codes are subgroups of \mathbb{Z}_{{2^s}}^n. These codes can be seen as a generalization of linear codes over 2 and 4. A {\mathbb{Z}_{{2^s}}}-linear code is a binary code, not necessarily linear, which is the Gray map image of a {\mathbb{Z}_{{2^s}}}-additive code. In 2014, a systematic encoding was found for 4-linear codes. Moreover, an alternative permutation decoding method, which is suitable for any binary code (not necessarily linear) with a systematic encoding, was established. In this paper, we generalise these results by presenting a systematic encoding for {\mathbb{Z}_{{2^s}}}-linear codes with s > 2. This encoding allows us to perform a permutation decoding for this family of codes.

Original languageEnglish
Title of host publicationProceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages140-144
Number of pages5
ISBN (Electronic)9781665402873
DOIs
Publication statusPublished - 11 Oct 2020

Publication series

NameProceedings of the 17th International Workshop on Algebraic and Combinatorial Coding Theory, ACCT 2020

Keywords

  • Gray map
  • systematic encoding
  • Z-additive codes
  • Z-linear codes

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