Results 251 to 260 of about 30,282 (293)
Association schemes related to Kasami codes and Kerdock sets.
Dam, E.R. van, Caen, D. de
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Canadian Journal of Mathematics, 1982 An ovoid in an orthogonal vector space V of type Ω+(2n, q) or Ω(2n – 1, q) is a set Ω of qn–1 + 1 pairwise non-perpendicular singular points. Ovoids probably do not exist when n > 4 (cf. [12], [6]) and seem to be rare when n = 4. On the other hand, when n = 3 they correspond to affine translation planes of order q2, via the Klein correspondence ...
William M. Kantor
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The Translation Planes of Dempwolff
Canadian Journal of Mathematics, 1981 In [2], Dempwolff constructs three translation planes of order 16 using sharply 2-transitive sets of permutations in S16. That is, if acting on Λ is a sharply 2-transitive set of permutations then an affine plane of order n may be defined as follows: The set of points = {(x, y)|x, y ∊ Λ} and the lines = {(x, y)|y = xg for fixed }, {(x, y)|x = c}, {(x,
N. L. Johnson
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A Classification of Semi-Translation Planes
Canadian Journal of Mathematics, 1969 The classification of certain types of projective planes has recently been of considerable interest to both geometers and group theorists. Due in part to the current general interest in finite mathematics and the developments connecting group theory and finite geometry, the Lenz-Barlotti classification of finite projective planes (2; 10), in particular,
Norman Lloyd Johnson
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The translation planes of order 49
Designs, Codes, and Cryptography, 1995The authors determine the quantity of classes of isomorphic translation planes of order 49. They report on the computer search for spreads in \(PG (3,7)\) and on classifying the spreads with the computer program NAUTY that looks for graph isomorphisms. The search results in a list of 1347 translation planes in which known planes formerly given by other
Rudolf Mathon, Gordon F Royle
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Doubly β-Derived Translation Planes
Designs, Codes and Cryptography, 2003 Let \(q>3\) be an odd prime power. A chain of circles in the Miquelian inversive plane \(M(q)\) is a collection of \({1\over 2}(q+3)\) circles such that every point covered by some circle in this set lies on exactly two circles from the collection. Using the correspondence between points and circles of \(M(q)\) and lines and reguli of a regular spread \
Abatangelo, V., Larato, Bambina
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A characterization of «likeable» translation planes
Rendiconti Del Circolo Matematico Di Palermo, 1983A translation plane of order \(q^ 2\) is said to be 'likeable' when it has kern \(GF(q)\) and when its linear translation complement contains a group of order \(q^ 2\) whose elation subgroup consists of elements, which, when the plane is constructed from a spread in \(PG(3,q)\), fix a regulus. Such planes are studied in this paper, mostly in terms of \(
N L Johnson, Johnson N L
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Translation planes of order 27
Designs, Codes, and Cryptography, 1994Up to isomorphism there are exactly seven, already known translation planes of order 27. The author shows this with the help of a computer and describes the seven types by invariants that play an important role in the computer search. Independently of the computer proof it is shown which of these types occur in the case that there is an elation in the ...
U Dempwolff
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, 2003 This monograph is about symplectic translation planes, with particular regard to those of even order. A characteristic property is the existence of completely regular line-ovals, which relies on some properties of classical groups, especially the symplectic and orthogonal ones.
MASCHIETTI, Antonio
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The translation planes of order 81 that admit SL(2,5), generated by affine elations
Journal of Geometry, 2006 The translation planes of order 81 admitting SL(2, 5), generated by affine elations, are completely determined. There are seven mutually non-isomorphic translation planes, of which five are new.
Norman L Johnson, Johnson Norman L
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