Enumerating alternating matrix spaces over finite fields with explicit coordinates

Enumerating permutation polynomials over finite fields by degree II

This note is a continuation of a paper by the same authors that appeared in 2002 in the same journal. First we extend the method of the previous paper proving an asymptotic formula for the number of permutations for which the associated permutation polynomial has d coefficients in specified fixed positions equal to 0. This also applies to the function Nq,d that counts the number of permutations...

Enumerating Permutation Polynomials over Finite Fields by Degree

fσ has the property that fσ(a) = σ(a) for every a ∈ Fq and this explains its name. For an account of the basic properties of permutation polynomials we refer to the book of Lidl and Niederreiter [5]. From the definition, it follows that for every σ ∂(fσ) ≤ q − 2. A variety of problems and questions regarding Permutation polynomials have been posed by Lidl and Mullen in [3, 4]. Among these there...

Random Krylov Spaces over Finite Fields

Motivated by a connection with block iterative methods for solving linear systems over finite fields, we consider the probability that the Krylov space generated by a fixed linear mapping and a random set of elements in a vector space over a finite field equals the space itself. We obtain an exact formula for this probability, and from it we derive good lower bounds that approach 1 exponentiall...

Matrix Theory over Finite Fields : A Survey

Recognizing finite matrix groups over infinite fields

Article history: Received 12 January 2012 Accepted 10 April 2012 Available online 15 June 2012