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Semifield Metrizability

open access: yesSemifield Metrizability
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Translation dual of a semifield

open access: yesJournal of Combinatorial Theory - Series A, 2008
A new description of the translation dual of a semifield introduced by \textit{G. Lunardon} [J. Geom. 76, No. 1--2, 200--215 (2003; Zbl 1042.51008)] is presented. Using this description, it is proved that a semifield and its translation dual have nuclei of the same order.
Rocco Trombetti   +2 more
exaly   +4 more sources
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On the Sporadic Semifield Flock

Designs, Codes and Cryptography, 2003
Let \(Q(4,q)\) denote the parabolic quadric of \(\text{ PG}(4,q)\). An ovoid of \(Q(4,q)\) is a set of \(q^2+1\) points of \(Q(4,q)\) such that no two of them are collinear (on a line of \(Q(4,q)\)). A BLT-set \(B\) is a set of \(q+1\) points of \(Q(4,q)\) such that no point of \(Q(4,q)\) is collinear with more than two points of \(B\).
Ilaria Cardinali   +2 more
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Infinite families of new semifields

Combinatorica, 2009
The authors construct six new infinite families of finite semifields, all of which are two-dimensional over their left nuclei. The semifields are given by providing spread sets of linear mappings. It is shown that semifields in different families are never isotopic. The classification of isotopy classes within a given family is still ongoing.
Gary L. Ebert   +3 more
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Algebraic extensions of semifields

Russian Mathematical Surveys, 2004
A semifield is a semiring \((D,+,\bullet)\) such that each nonzero element is invertible with repect to multiplication and is not invertible with respect to addition. In this paper, the author examines the possibility of extending a semifield by a root of an algebraic equation. Let \(D\) denote a semifield. Then \(D\) is called idempotent (cancellable)
openaire   +1 more source

Semifields and their properties

Journal of Mathematical Sciences, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vechtomov, E. M., Cheraneva, A. V.
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