Results 11 to 20 of about 645 (110)
On Translation Hyperovals in Semifield Planes [PDF]
Designs, Codes and Cryptography, 2023 In this paper we demonstrate the first example of a finite translation plane which does not contain a translation hyperoval, disproving a conjecture of Cherowitzo. The counterexample is a semifield plane, specifically a Generalised Twisted Field plane, of order $64$. We also relate this non-existence to the covering radius of two associated rank-metric
Kevin Allen, John Sheekey
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2-elements in an Autotopism Group of a Semifield Projective Plane
Известия Иркутского государственного университета: Серия "Математика", 2022 We investigate the well-known hypothesis of D.R. Hughes that the full collineation group of non-Desarguesian semifield projective plane of a finite order is solvable (the question 11.76 in Kourovka notebook was written down by N.D. Podufalov). The spread
Olga Kravtsova
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Hyperovals in Knuth's binary semifield planes [PDF]
European Journal of Combinatorics, 2016 In each of the three projective planes coordinatised by the Knuth's binary semifield $\mathbb{K}_n$ of order $2^n$ and two of its Knuth derivatives, we exhibit a new family of infinitely many translation hyperovals. In particular, when $n=5$, we also present complete lists of all translation hyperovals in them. The properties of some designs associated
Nicola Durante +2 more
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Semifield Planes Admitting the Quaternion Group Q8 [PDF]
Algebra i logika, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
О. В. Кравцова
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Elementary Abelian 2-subgroups in an Autotopism Group of a Semifield Projective Plane
Известия Иркутского государственного университета: Серия "Математика", 2020 Elementary Abelian 2-subgroups in an Autotopism Group of a Semifield Projective Plane} We investigate the hypotheses on a solvability of the full collineation group for non-Desarguesian semifield projective plane of a finite order (the question 11.76 in ...
O. V. Kravtsova
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Finite semifields and projective planes
Journal of Algebra, 1965 NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This paper makes contributions to the structure theory of finite semifields, i.e., of finite nonassociative division algebras with unit.
Donald E. Knuth
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The nuclei and other properties of p‐primitive semifield planes [PDF]
, 1992 Publisher Summary This chapter present a study of the class of semifield planes of order p4 and kernel GF(p2) with the property that they admit a p-primitive Baer collineation; these are called “p-primitive semifield planes.”This is the class of planes obtained when the construction method of Hiramine, Matsumoto, and Oyama is applied to the ...
Minerva Cordero
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New Semifield Planes of order 81 [PDF]
, 2008 14 pages. Revised paper (original title: New semifield planes of orders 64 and 81). U. Dempwolff had previously and independently obtained a classification of finite semifields of order 81 (Semifield Planes of Order 81, J. of Geometry (to appear)).
I. F. Rúa, Elías F. Combarro
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Autotopism groups of cyclic semifield planes [PDF]
Journal of Algebraic Combinatorics, 2011 Let \(V\) be an \(m\)-dimensional vector space over the finite field \(K\) with \(q^{n}\) elements, \(\sigma\) an automorphism of \(K\) and \(T\) an irreducible \(\sigma\)-linear operator on \(V\). Assume that the fixed field \(K_{0}\) of \(\sigma\) has \(q=p^{f}\) elements, \(p\) prime.
Ulrich Dempwolff
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Matrix spread sets of p‐primitive semifield planes [PDF]
International Journal of Mathematics and Mathematical Sciences, 1995 In this article we present the matrix spread sets of the p‐primitive planes of order p4 where p = 3, 5, 7, 11.
Minerva Cordero
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