31 citations · 64 across the 19 of their papers we have counts for
21 papers
On the Weil descent of Artin-Schreier algebraic function fields over finite fields
Stéphane Ballet, Robert Rolland
Let us consider a generalized Artin-Schreier algebraic function field extension of the rational function field $\F_{p^n}(x)$ defined over the finite field extension $K=\F_{p^n}…
Chaining Multiplications in Finite Fields with Chudnovsky-type Algorithms and Tensor Rank of the k-multiplication
Stéphane Ballet, Robert Rolland
We design a class of Chudnovsky-type algorithms multiplying k elements of a finite extension of order n a finite field K. We prove that these algorithms give a tensor decomposition…
Optimization of the scalar complexity of Chudnovsky multiplication algorithms in finite fields
Stephane Ballet, Alexis Bonnecaze, Thanh-Hung Dang
We propose several constructions for the original multiplication algorithm of D.V. and G.V. Chudnovsky in order to improve its scalar complexity. We highlight the set of generic st…
Multiplication in finite fields with Chudnovsky-type algorithms on the projective line
Stéphane Ballet, Alexis Bonnecaze, Bastien Pacifico
We propose a Recursive Polynomial Generic Construction (RPGC) of multiplication algorithms in any finite field based on the method of D.V. and G.V. Chudnovsky sp…
On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry
Stéphane Ballet, Jean Chaumine, Julia Pieltant +3
In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite extensions of finite fields, enriched with some not published recent…
Dense families of modular curves, prime numbers and uniform symmetric tensor rank of multiplication in certain finite fields
Stéphane Ballet, Alexey Zykin
We obtain new uniform bounds for the symmetric tensor rank of multiplication in finite extensions of any finite field Fp or Fp2 where p denotes a prime number greater or equal than…