Modified quadratic residue constructions and new extremal binary self-dual codes of lengths 64, 66 and 68

Joe Gildea, Holly Hamilton, Abidin Kaya, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this work we consider modified versions of quadratic double circulant and quadratic bordered double circulant constructions over the binary field and the rings F2+uF2 and F4+uF4 for different prime values of p. Using these constructions with extensions and neighbors we are able to construct a number of extremal binary self-dual codes of different lengths with new parameters in their weight enumerators. In particular we construct 2 new codes of length 64, 4 new codes of length 66 and 14 new codes of length 68. The binary generator matrices of the new codes are available online at [8].

Original languageEnglish (US)
Article number105927
JournalInformation Processing Letters
Volume157
DOIs
StatePublished - May 2020

Keywords

  • Codes over rings
  • Combinatorial problems
  • Extremal self-dual codes
  • Quadratic circulant matrices
  • Quadratic residues

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

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