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

Akihiro Munemasa; Vladimir D. Tonchev

doi:10.1002/jcd.21740

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

Akihiro Munemasa, Vladimir D. Tonchev

情報科学研究科・情報基礎科学専攻

研究成果: Article › 査読

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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.

本文言語	English
ページ（範囲）	745-752
ページ数	8
ジャーナル	Journal of Combinatorial Designs
巻	28
号	10
DOI	https://doi.org/10.1002/jcd.21740
出版ステータス	Published - 2020 10月 1

ASJC Scopus subject areas

離散数学と組合せ数学

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10.1002/jcd.21740

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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.",

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N2 - 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.

AB - 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.

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KW - linear code

KW - quasi-3 design

KW - quasisymmetric design

KW - residual design

KW - symmetric design

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

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