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arXiv · 2003.04453

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

Akihiro Munemasa·Vladimir D. Tonchev
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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 quasi-symmetric 2-$(56,12,9)$ and 2-$(57,12,11)$ designs with intersection numbers 0 and 3, and the nonexistence of a 2-$(267,57,12)$ quasi-3 design. The nonexistence of a 2-$(149,37,9)$ quasi-3 design is also proved.

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Akihiro Munemasa, Vladimir D. Tonchev. 2020-06-08. Ternary codes, biplanes, and the nonexistence of some quasi-symmetric and quasi-3 designs. https://arxiv.org/abs/2003.04453

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