New extremal binary self-dual codes of length 68 from quadratic residue codes over F 2 + uF 2 + u 2F 2

Abidin Kaya, Bahattin Yildiz, Irfan Siap

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

In this work, quadratic residue codes over the ring F2+u F2+u2F2 with u3=u are considered. A duality and distance preserving Gray map from F2+uF2+ u2F2 to F23 is defined. By using quadratic double circulant, quadratic bordered double circulant constructions and their extensions self-dual codes of different lengths are obtained. As Gray images of these codes and their extensions, a substantial number of new extremal self-dual binary codes are found. More precisely, thirty two new extremal binary self-dual codes of length 68, 363 Type I codes of parameters [72,36,12], a Type II [72,36,12] code and a Type II [96,48,16] code with new weight enumerators are obtained through these constructions. The results are tabulated.

Original languageEnglish (US)
Pages (from-to)160-177
Number of pages18
JournalFinite Fields and Their Applications
Volume29
DOIs
StatePublished - Sep 2014
Externally publishedYes

Keywords

  • Extremal self-dual codes
  • Gray maps
  • Quadratic double-circulant codes
  • Quadratic residue codes

ASJC Scopus subject areas

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

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