8 research outputs found
On symplectic semifield spreads of PG(5,q2), q odd
We prove that there exist exactly three non-equivalent symplectic semifield spreads of PG ( 5 , q2), for q2> 2 .38odd, whose associated semifield has center containing Fq. Equivalently, we classify, up to isotopy, commutative semifields of order q6, for q2> 2 .38odd, with middle nucleus containing q2Fq2and center containing q Fq
Finite semifields and nonsingular tensors
In this article, we give an overview of the classification results in the theory of finite semifields (note that this is not intended as a survey of finite semifields including a complete state of the art (see also Remark 1.10)) and elaborate on the approach using nonsingular tensors based on Liebler (Geom Dedicata 11(4):455-464, 1981)
On isotopisms and strong isotopisms of commutative presemifields
In this paper we prove that the ( odd prime power and
odd) commutative semifields constructed by Bierbrauer in \cite{BierbrauerSub}
are isotopic to some commutative presemifields constructed by Budaghyan and
Helleseth in \cite{BuHe2008}. Also, we show that they are strongly isotopic if
and only if . Consequently, for each
there exist isotopic commutative presemifields of order (
odd) defining CCZ--inequivalent planar DO polynomials.Comment: References updated, pag. 5 corrected Multiplication of commutative
LMPTB semifield
On BEL-configurations and finite semifields
The BEL-construction for finite semifields was introduced in \cite{BEL2007};
a geometric method for constructing semifield spreads, using so-called
BEL-configurations in . In this paper we investigate this construction
in greater detail, and determine an explicit multiplication for the semifield
associated with a BEL-configuration in , extending the results from
\cite{BEL2007}, where this was obtained only for . Given a
BEL-configuration with associated semifields spread , we also show
how to find a BEL-configuration corresponding to the dual spread
. Furthermore, we study the effect of polarities in on
BEL-configurations, leading to a characterisation of BEL-configurations
associated to symplectic semifields.
We give precise conditions for when two BEL-configurations in
define isotopic semifields. We define operations which preserve the BEL
property, and show how non-isotopic semifields can be equivalent under this
operation. We also define an extension of the ```switching'' operation on
BEL-configurations in introduced in \cite{BEL2007}, which, together
with the transpose operation, leads to a group of order acting on
BEL-configurations
Classification and computational search for planar functions in characteristic 3
Masteroppgave i informatikkINF399MAMN-PROGMAMN-IN
Semifields of order q^6 with left nucleus F_{q^3} and center F_q
In [G. Marino, O. Polverino, R. Trombetti, On Fq-linear sets of PG(3,q3) and semifields, J. Combin.
Theory Ser. A 114 (5) (2007) 769–788] it has been proven that there exist six non-isotopic families Fi
(i=0,...,5)ofsemifieldsoforderq6withleftnucleusFq3 andcenterFq,accordingtothedifferentgeo-
metric configurations of the associated Fq -linear sets. In this paper we first prove that any semifield of order
q6 with left nucleus Fq3 , right and middle nuclei Fq2 and center Fq is isotopic to a cyclic semifield. Then,
we focus on the family F4 by proving that it can be partitioned into three further non-isotopic families:
F (a) , F (b) , F (c) and we show that any semifield of order q 6 with left nucleus F 3 , right and middle nuclei 444 q
F 2 and center Fq belongs to the family F(c). q4
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