Results 11 to 20 of about 109 (103)
Generalized semifield spreads [PDF]
Designs, Codes and Cryptography, 2022 A partition \(\Omega = \{A_1, \dots, A_K\}\), of \(\mathrm{GF}(p^n)\) (regarded as a \(\mathrm{GF}(p)\)-vector space) into \(K\) subsets is called a \textit{bent partition} of \textit{depth} \(K\), if every function \(f : \mathrm{GF}(p^n)\to \mathrm{GF}(p)\) for which the following property holds, is a bent function: The preimage set of any element \(c\
Nurdagül Anbar +2 more
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Switchings of semifield multiplications [PDF]
Designs, Codes and Cryptography, 2015 Let $B(X,Y)$ be a polynomial over $\mathbb{F}_{q^n}$ which defines an $\mathbb{F}_q$-bilinear form on the vector space $\mathbb{F}_{q^n}$, and let $ξ$ be a nonzero element in $\mathbb{F}_{q^n}$. In this paper, we consider for which $B(X,Y)$, the binary operation $xy+B(x,y)ξ$ defines a (pre)semifield multiplication on $\mathbb{F}_{q^n}$.
Xiang-dong Hou +2 more
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Discussiones Mathematicae - General Algebra and Applications, 2004 Summary: It is well known that a semigroup \(S\) is a Clifford semigroup if and only if \(S\) is a strong semilattice of groups. We have recently extended this important result from semigroups to semirings by showing that a semiring \(S\) is a Clifford semiring if and only if \(S\) is a strong distributive lattice of skew-rings.
Sen, Mridul K. +2 more
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Discussiones Mathematicae - General Algebra and Applications, 2004 Summary: We introduce the notions of ternary semi-integral domain and ternary semifield and study some of their properties. In particular we also investigate the maximal ideals of the ternary semiring \(\mathbb{Z}^-_0\).
Dutta, Tapan K., Kar, Sukhendu
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Journal of Combinatorial Theory, Series A, 1999 \textit{T. Penttila} and \textit{B. Williams} [Geom. Dedicata, to appear] have constructed a sporadic translation ovoid of the quadrangle \(Q(4, 3^5)\). Associated with this, there is a new (semifield) flock of a quadratic cone in \(\text{PG}(3,3^5)\), and hence a flock generalized quadrangle of order \((3^5,3^{10})\).
BADER, LAURA +2 more
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Translation dual of a semifield
Journal 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.
LUNARDON, GUGLIELMO +3 more
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On the classification of semifield flocks
Advances in Mathematics, 2003 The main result of this paper is the following one: Let \({\mathcal F}\) be a flock of a quadratic cone over the field \(\text{GF}(g^n)\) associated with a semifield plane with kernel \(\text{GF}(q)\), and such that \(q\geq 4n^2- 8n+ 2\), then \({\mathcal F}\) is a linear flock (all planes of the flock contain a fixed line), or a Kantor-Knuth flock ...
BLOKHUIS A, LAVRAUW, MICHEL, BALL S.
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On automorphisms of semifields and semifield planes
Sibirskie Elektronnye Matematicheskie Izvestiya, 2016 Изучается взаимосвязь полуполевой проективной плоскости и ее координатизирующего полуполя с использованием линейного пространства и регулярного множества. Установлен геометрический смысл инволюторного автоморфизма конечного полуполя, доказаны некоторые его свойства.
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Discrete Mathematics, 1999 An algebraic system \(S\) with two binary operations (addition and multiplication) is called a semifield if the following axioms are fulfilled: 1. \((S;+)\) is a group with identity \(0\). 2. If \(a,b\in S\) and \(ab=0\) then \(a=0\) or \(b=0\). 3. If \(a,b,c\in S\) then \(a(b+c)=ab+ac\) and \((a+b)c=ac+bc\). 4.
Minerva Cordero, Gregory P. Wene
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