On primitive elements in finite semifields
نویسندگان
چکیده
منابع مشابه
Finite semifields
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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We discuss the problem of constructing a small subset of a finite field containing primitive elements of the field. Given a finite field, Fqn , small q and large n, we show that the set of all low degree polynomials contains the expected number of primitive elements. The main theorem we prove is a bound for character sums over short intervals in function fields. Our result is unconditional and ...
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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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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...
متن کاملSegre embeddings and finite semifields
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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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2011
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2010.11.003