New extremal binary self-dual codes from a Baumert–Hall array

Abidin Kaya, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review

Abstract

In this work, we introduce new construction methods for self-dual codes using a Baumert–Hall array. We apply the constructions over the alphabets F2 and F4+uF4 and combine them with extension theorems and neighboring constructions. As a result, we construct 46 new extremal binary self-dual codes of length 68, 26 new best known Type II codes of length 72 and 8 new extremal Type II codes of length 80 that lead to new 3−(80,16,665) designs. Among the new codes of length 68 are the examples of codes with the rare γ=5 parameter in W68,2. All these new codes are tabulated in the paper.

Original languageEnglish (US)
Pages (from-to)74-83
Number of pages10
JournalDiscrete Applied Mathematics
Volume271
DOIs
StatePublished - Dec 1 2019
Externally publishedYes

Keywords

  • Baumert–Hall array
  • Codes over rings
  • Extension theorems
  • Extremal self-dual codes
  • Gray maps

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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