Affine geometry designs, polarities, and Hamada's conjecture

DOI10.1016/j.jcta.2010.06.007zbMath1292.05055OpenAlexW1964973604WikidataQ123363089 ScholiaQ123363089MaRDI QIDQ616453

Dieter Jungnickel, Vladimir D. Tonchev, David Clark

Publication date: 7 January 2011

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2010.06.007

zbMATH Keywords

designaffine geometrypolarityHamada's conjecture

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Combinatorial codes (94B25)

Related Items (10)

The weight distribution of the self-dual \([128,64\) polarity design code] ⋮ Linearly embeddable designs ⋮ Extension sets, affine designs, and Hamada's conjecture ⋮ Characterizing geometric designs. II. ⋮ Recent results on designs with classical parameters ⋮ Almost perfect and planar functions ⋮ A Hamada type characterization of the classical geometric designs ⋮ New invariants for incidence structures ⋮ Exponential bounds on the number of designs with affine parameters ⋮ Correction to: “Exponential bounds on the number of designs with affine parameters”

Cites Work

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• The twisted Grassmann graph is the block graph of a design
• On the p-rank of the incidence matrix of a balanced or partially balanced incomplete block design and its applications to error correcting codes
• Polarities, quasi-symmetric designs, and Hamada's conjecture
• Quasi-symmetric \(2\text{-}(31,7,7)\) designs and a revision of Hamada's conjecture
• A new family of distance-regular graphs with unbounded diameter
• Majority logic decoding using combinatorial designs (Corresp.)
• A class of majority logic decodable codes (Corresp.)

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