Planes of order 10 do not have a collineation of order 5

DOI10.1016/0097-3165(80)90046-1zbMath0442.05013OpenAlexW2055612569MaRDI QIDQ1143397

Richard P. Anstee, Marshall jun. Hall, John G. Thompson

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1016/0097-3165(80)90046-1

zbMATH Keywords

projective planecodecollineation20 point settwenty point set

Mathematics Subject Classification ID

Combinatorial aspects of finite geometries (05B25) Combinatorial codes (94B25) Non-Desarguesian affine and projective planes (51A35)

Related Items (12)

Unnamed Item ⋮ The nonexistence of a certain Steiner system S(3,12,112) ⋮ Codes and designs ⋮ Cycle decompositions of complete graphs ⋮ On projective planes of type (5,m) ⋮ On primes dividing the group order of a doubly-even \((72,36,16)\) code and the group order of a quaternary \((24,12,10)\) code ⋮ Codes and designs -- existence and uniqueness ⋮ On the automorphism group of a binary \(q\)-analog of the Fano plane ⋮ The extremal codes of length 42 with automorphism of order 7 ⋮ Some of the finite projective planes ⋮ On vectors of weight 16 in the code of a projective plane of order 10 ⋮ Variations on seven points: An introduction to the scope and methods of coding theory and finite geometries

Cites Work

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• Generalized incidence matrices over group algebras
• Collineations of projective planes of order 10, part II
• On the existence of a projective plane of order 10
• Collineations and Generalized Incidence Matrices
• On the classification and enumeration of self-dual codes

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