Constructing self-dual codes from group rings and reverse circulant matrices

Joe Gildea, Adrian Korban, Abidin Kaya, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this work, we describe a construction for self-dual codes in which we employ group rings and reverse circulant matrices. By applying the construction directly over different alphabets, and by employing the well known extension and neighbor methods we were able to obtain extremal binary selfdual codes of different lengths of which some have parameters that were not known in the literature before. In particular, we constructed three new codes of length 64, twenty-two new codes of length 68, twelve new codes of length 80 and four new codes of length 92.

Original languageEnglish (US)
Pages (from-to)471-485
Number of pages15
JournalAdvances in Mathematics of Communications
Volume15
Issue number3
DOIs
StatePublished - 2021

Keywords

  • Codes over rings
  • Extremal binary self-dual codes
  • Group ring
  • Reverse circulant matrices

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computer Networks and Communications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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