Finite Fields and Their Applications

Isomorphism classes of hyperelliptic curves of genus 3 over finite fields

We give the number of the isomorphism classes of hyperelliptic curves of genus 3 defined over finite fields Fpn , p 6= 2, 7. These results have applications to cryptography.

New Kloosterman sum identities and equalities over finite fields

We present some general equalities between Kloosterman sums over finite fields of arbitrary characteristics. In particular, we obtain an explicit Kloosterman sum identity over finite fields of characteristic 3. © 2008 Elsevier Inc. All rights reserved.

Factors of Dickson polynomials over finite fields

We give new descriptions of the factors of Dickson polynomials over finite fields.

The Splitting Subspace Conjecture

We answer a question by Niederreiter concerning the enumeration of a class of subspaces of finite dimensional vector spaces over finite fields by proving a conjecture by Ghorpade and Ram.

Torsion of abelian varieties over large algebraic fields

Finite field models in arithmetic combinatorics - ten years on