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

DOI10.1002/jcd.21740arXiv2003.04453OpenAlexW3037660683MaRDI QIDQ6146770

Akihiro Munemasa, Vladimir D. Tonchev

Publication date: 31 January 2024

Published in: Journal of Combinatorial Designs (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.04453

zbMATH Keywords

symmetric designlinear coderesidual designbiplanequasisymmetric designquasi-3 design

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Linear codes (general theory) (94B05)

Cites Work

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• A new biplane of order 9 with a small automorphism group
• Geometric invariants for quasi-symmetric designs
• The four known biplanes with k=11
• Linearly embeddable designs
• Fundamentals of Error-Correcting Codes
• Self‐Dual Codes and the Nonexistence of a Quasi‐Symmetric 2‐(37,9,8) Design with Intersection Numbers 1 and 3
• There are exactly five biplanes with k = 11
• Designs derived from permutation groups
• An Embedding Theorem for Balanced Incomplete Block Designs

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