Constructions for self-dual codes induced from group rings

Joe Gildea, Abidin Kaya, Rhian Taylor, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

In this work, we establish a strong connection between group rings and self-dual codes. We prove that a group ring element corresponds to a self-dual code if and only if it is a unitary unit. We also show that the double-circulant and four-circulant constructions come from cyclic and dihedral groups, respectively. Using groups of order 8 and 16 we find many new construction methods, in addition to the well-known methods, for self-dual codes. We establish the relevance of these new constructions by finding many extremal binary self-dual codes using them, which we list in several tables. In particular, we construct 10 new extremal binary self-dual codes of length 68.

Original languageEnglish (US)
Pages (from-to)71-92
Number of pages22
JournalFinite Fields and Their Applications
Volume51
DOIs
StatePublished - May 2018

Keywords

  • Codes over rings
  • Group rings
  • Self-dual codes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering(all)
  • Applied Mathematics

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