The translation planes of order 49

DOI10.1007/BF01388504zbMath0819.51003OpenAlexW2095245134MaRDI QIDQ1344526

Gordon F. Royle, Rudolf A. Mathon

Publication date: 13 February 1995

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01388504

zbMATH Keywords

spreadsregulusisomorphic translation planesorder 49

Mathematics Subject Classification ID

Computing methodologies and applications (68U99) Translation planes and spreads in linear incidence geometry (51A40)

Related Items (15)

Ovoids of the quadric Q\((2n,q)\) ⋮ On incidence structures of nonsingular points and hyperbolic lines of ovoids in finite orthogonal spaces ⋮ Two-graphs and skew two-graphs in finite geometries ⋮ Constructions and bounds for mixed-dimension subspace codes ⋮ On the transposed Rao's flag-transitive plane of order 49 ⋮ Symplectic spreads in \(PG(3,q)\), inversive planes and projective planes ⋮ The eight dimensional ovoids over GF(5) ⋮ Linear groups as right multiplication groups of quasifields ⋮ The translation planes of order 49 and their automorphism groups ⋮ On ovoids of parabolic quadrics ⋮ On the smallest minimal blocking sets of \(Q(2n,q)\), for \(q\) an odd prime ⋮ A lower bound for the minimum weight of the dual 7-ary code of a projective plane of order 49 ⋮ Symplectic semifield planes and ℤ₄–linear codes ⋮ An orderly algorithm and some applications in finite geometry ⋮ Twisted quadrics and \(\alpha\)-flocks

Uses Software

• nauty
• Cayley

Cites Work

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• A translation plane of order \(7^ 2\) with a very small translation complement
• The classification of the translation planes of order 16. I
• A translation plane of order 49 with non-solvable collineation group
• Some finite translation planes arising from \(A_ 6\)-invariant ovoids of the Klein quadric
• Some translation planes of order \(p^ 2\) and of extra-special type
• Some translation planes of order \(7^ 2\) which admit \(SL_ 2(9)\)
• Translationsebenen der Ordnung 49 mit Scherungen. (On translation planes of order 49 admitting shears.)
• The translation planes of order twenty-five
• Translationsebenen der Ordnung 49 mit einer Quaternionengruppe von Dehnungen. (Translation planes of order 49 with a quaternion group of homologies)
• Inversive geometry and some new translation planes. I
• Translation planes of order 27
• Two-graphs and skew two-graphs in finite geometries
• Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe

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