Self-Dual Codes and the Nonexistence of a Quasi-Symmetric 2-(37,9,8) Design with Intersection Numbers 1 and 3

Masaaki Harada, Akihiro Munemasa, Vladimir D. Tonchev

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We prove that a certain binary linear code associated with the incidence matrix of a quasi-symmetric 2-(37, 9, 8) design with intersection numbers 1 and 3 must be contained in an extremal doubly even self-dual code of length 40. Using the classification of extremal doubly even self-dual codes of length 40, we show that a quasi-symmetric 2-(37, 9, 8) design with intersection numbers 1 and 3 does not exist.

Original languageEnglish
Pages (from-to)469-476
Number of pages8
JournalJournal of Combinatorial Designs
Volume25
Issue number10
DOIs
Publication statusPublished - 2017 Oct

Keywords

  • doubly even self-dual code
  • quasi-symmetric 2-design
  • self-orthogonal code

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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