Divisible designs from semifield planes
نویسندگان
چکیده
منابع مشابه
Construction of Divisible Designs from Translation Planes
We construct some classes of divisible designs from nite translation planes of dimension two and three over GF(q), q a prime power, admitting SL(2; q) as a collineation group.
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In 1965 Knuth [17] noticed that a finite semifield was determined by a 3-cube array (aijk) and that any permutation of the indices would give another semifield. In this article we explain the geometrical significance of these permutations. It is known that a pair of functions (f, g) where f and g are functions from GF (q) to GF (q) with the property that f and g are linear over some subfield an...
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"We investigateof the all-ones matrix .]V for1) 16 over va,rious admissible groups. For 1) 16 allhave been PIlumera,ted. For the case 7) 16 only some classes have been completely enumerated. Of particularare signings over the group since these can alsobe considHed as GDD(16 X 2,16,these overexpanding,GDD(16 4,16,4)'s. We continne in this way until we obtainG ...
متن کاملAutotopism groups of cyclic semifield planes
In this article we investigate the autotopism group of the so-called cyclic semifield planes. We show that the group generated by the homology groups of the nuclei is already the full group of autotopisms that are linear with respect to the nuclei. The full autotopism group is also computed with the exception of one special subcase.
متن کاملNew Semifield Planes of order 81 ∗
A finite semifield D is a finite nonassociative ring with identity such that the set D∗ = D \ {0} is closed under the product. From any finite semifield a projective plane can be constructed. In this paper we obtain new semifield planes of order 81 by means of computational methods. These computer-assisted results yield to a complete classification (up to isotopy) of 81-element finite semifields.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00386-7