New extremal binary self-dual codes from a modified four circulant construction

Abidin Kaya, Bahattin Yildiz, Abdullah Pasa

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

In this work, we propose a modified four circulant construction for self-dual codes and a bordered version of the construction using the properties of λ-circulant and λ-reverse circulant matrices. By using the constructions on F2, we obtain new binary codes of lengths 64 and 68. We also apply the constructions to the ring R2 and considering the F2 and R1-extensions, we obtain new singly-even extremal binary self-dual codes of lengths 66 and 68. More precisely, we find 3 new codes of length 64, 13 new codes of length 66 and 21 new codes of length 68. These codes all have weight enumerators with parameters that were not known to exist in the literature.

Original languageEnglish (US)
Pages (from-to)1086-1094
Number of pages9
JournalDiscrete Mathematics
Volume339
Issue number3
DOIs
StatePublished - Mar 6 2016
Externally publishedYes

Keywords

  • Circulant matrices
  • Extremal self-dual codes
  • Four circulant construction
  • Reverse-circulant matrices

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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