New self-dual and formally self-dual codes from group ring constructions

Steven T. Dougherty, Joe Gildea, Abidin Kaya, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this work, we study construction methods for self-dual and formally self-dual codes from group rings, arising from the cyclic group, the dihedral group, the dicyclic group and the semi-dihedral group. Using these constructions over the rings F2 + uF2 and F4 + uF4, we obtain 9 new extremal binary self-dual codes of length 68 and 25 even formally self-dual codes with parameters [72, 36, 14].

Original languageEnglish (US)
Pages (from-to)11-22
Number of pages12
JournalAdvances in Mathematics of Communications
Volume14
Issue number1
DOIs
StatePublished - Feb 2020

Keywords

  • Codes over rings
  • Extremal codes
  • Formally self-dual codes
  • Group rings
  • Self-dual codes

ASJC Scopus subject areas

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

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