New extremal binary self-dual codes of length 68 from generalized neighbors

Joe Gildea, Abidin Kaya, Adrian Korban, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In this work, we use the concept of distance between self-dual codes, which generalizes the concept of a neighbor for self-dual codes. Using the k-neighbors, we are able to construct extremal binary self-dual codes of length 68 with new weight enumerators. We construct 143 extremal binary self-dual codes of length 68 with new weight enumerators including 42 codes with γ=8 in their W68,2 and 40 with γ=9 in their W68,2. These examples are the first in the literature for these γ values. This completes the theoretical list of possible values for γ in W68,2.

Original languageEnglish (US)
Article number101727
JournalFinite Fields and Their Applications
Volume67
DOIs
StatePublished - Oct 2020

Keywords

  • Distance of self-dual codes
  • Extremal self-dual codes
  • Neighbor
  • Weight enumerator
  • kth neighbor

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • General Engineering
  • Applied Mathematics

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