Stéphane Ballet

Quasi-optimal algorithms for multiplication in the extensions of F16 of degree 13, 14 and 15

Abstract From an interpolation method on algebraic curves, due to Chudnovsky and Chudnovsky, we construct effective bilinear algorithms for multiplication in the extensions of F 16 of degree 13⩽n⩽15, with a bilinear complexity equal to 2n+1. These algorithms which are the first hyperelliptic algorithms of multiplication, are obtained from the hyperelliptic curve of genus 2 with plane equation y2+y=x5.

On low weight codewords of generalized affine and projective Reed---Muller codes

We propose new results on low weight codewords of affine and projective generalized Reed–Muller (GRM) codes. In the affine case we prove that if the cardinality of the ground field is large compared to the degree of the code, the low weight codewords are products of affine functions. Then, without this assumption on the cardinality of the field, we study codewords associated to an irreducible but not absolutely irreducible polynomial, and prove that they cannot be second, third or fourth weight depending on the hypothesis. In the projective case the second distance of GRM codes is estimated, namely a lower bound and an upper bound on this weight are given.

On the existence of dimension zero divisors in algebraic function fields defined over F_q.

Let

On the construction of elliptic Chudnovsky-type algorithms for multiplication in large extensions of finite fields

\mathbf{F}/\mathbb{F}_q

Shimura Modular Curves and Asymptotic Symmetric Tensor Rank of Multiplication in any Finite Field

be an algebraic function field of genus

A note on Yao's theorem about pseudo-random generators

g

Dense families of modular curves, prime numbers and uniform symmetric tensor rank of multiplication in certain finite fields

defined over a finite field

Arithmetic in finite fields based on the Chudnovsky-Chudnovsky multiplication algorithm

\mathbb{F}_q

Native plant species richness on Eastern Polynesia’s remote atolls: Which abiotic factors influence its spatial pattern?

. We obtain new results on the existence, the number and the density of dimension zero divisors of degree

Algorithmic Arithmetic, Geometry, and Coding Theory

g-k