Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes

Steven T. Dougherty, Joseph Gildea, Adrian Korban, Abidin Kaya, Alexander Tylyshchak, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We introduce a bordered construction over group rings for self-dual codes. We apply the constructions over the binary field and the ring F 2 +uF 2 , using groups of orders 9, 15, 21, 25, 27, 33 and 35 to find extremal binary self-dual codes of lengths 20, 32, 40, 44, 52, 56, 64, 68, 88 and best known binary self-dual codes of length 72. In particular we obtain 41 new binary extremal self-dual codes of length 68 from groups of orders 15 and 33 using neighboring and extensions. All the numerical results are tabulated throughout the paper.

Original languageEnglish (US)
Pages (from-to)108-127
Number of pages20
JournalFinite Fields and Their Applications
Volume57
DOIs
StatePublished - May 2019

Keywords

  • Bordered constructions
  • Codes over rings
  • Extremal codes
  • Group rings
  • Self-dual codes

ASJC Scopus subject areas

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

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