Ternary codes, biplanes, and the nonexistence of some quasisymmetric and quasi-3 designs

Akihiro Munemasa, Vladimir D. Tonchev

Research output: Contribution to journalArticlepeer-review

Abstract

The dual codes of the ternary linear codes of the residual designs of biplanes on 56 points are used to prove the nonexistence of quasisymmetric 2- (Formula presented.) and 2- (Formula presented.) designs with intersection numbers 0 and 3, and the nonexistence of a 2- (Formula presented.) quasi-3 design. The nonexistence of a 2- (Formula presented.) quasi-3 design is also proved.

Original languageEnglish
Pages (from-to)745-752
Number of pages8
JournalJournal of Combinatorial Designs
Volume28
Issue number10
DOIs
Publication statusPublished - 2020 Oct 1

Keywords

  • biplane
  • linear code
  • quasi-3 design
  • quasisymmetric design
  • residual design
  • symmetric design

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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