The homogeneous weight for Rk, related gray map and new binary quasi-cyclic codes

Bahattin Yildiz, Ismail Gokhan Kelebek

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Using theoretical results about the homogeneous weights for Frobenius rings, we describe the homogeneous weight for the ring family Rk, a recently introduced family of Frobenius rings which have been used extensively in coding theory. We find an associated Gray map for the homogeneous weight using first order Reed-Muller codes and we describe some of the general properties of the images of codes over Rk under this Gray map. We then discuss quasi-twisted codes over Rk and their binary images under the homogeneous Gray map. In this way, we find many optimal binary codes which are self-orthogonal and quasi-cyclic. In particular, we find a substantial number of optimal binary codes that are quasi-cyclic of index 8, 16 and 24, nearly all of which are new additions to the database of quasi-cyclic codes kept by Chen.

Original languageEnglish (US)
Pages (from-to)885-897
Number of pages13
JournalFilomat
Volume31
Issue number4
DOIs
StatePublished - 2017
Externally publishedYes

Keywords

  • Codes over rings
  • Cyclic codes
  • Homogeneous weights
  • Quasi-cyclic codes
  • Quasi-twisted codes

ASJC Scopus subject areas

  • General Mathematics

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