The BEL-rank of finite semifields
نویسندگان
چکیده
منابع مشابه
On BEL-configurations and finite semifields
In this talk we will explain the Knuth orbit of a semifield S: a set of six isotopism classes of semifields associated to S (from [2]), and discuss ways of extending it, using techniques from finite geometry. A BEL-configuration in Frn q is a triple (D, U,W ), where D is a Desarguesian spread, and U and W are subspaces of dimension n and rn− n, resp., such that no element of D intesects both U ...
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This note surveys the known finite semifields and discusses the question: How many finite semifields of a given order are there up to isotopism?
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Each embedded product space PG(n, q)×PG(n, q) in an (n2 +n− 1)-dimensional projective space is obtained by projecting the Segre variety Sn,n,q from an n-subspace δ skew with its first secant variety. On the other hand, when δ is skew with the (n − 1)-th secant variety, it determines a semifield of order qn+1 whose center contains Fq. A relationship arises between a particular class of embedding...
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In this article, we give an overview of the classification results in the theory of finite semifieldsand elaborate on the approach using nonsingular tensors based on Liebler [52].
متن کاملOn the isotopism classes of finite semifields
A projective plane is called a translation plane if there exists a line L such that the group of elations with axis L acts transitively on the points not on L. A translation plane whose dual plane is also a translation plane is called a semifield plane. The ternary ring corresponding to a semifield plane can be made into a non-associative algebra called a semifield, and two semifield planes are...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2016
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-016-0270-z