Philippe Langevin

activity

20122023

collaborators

7 papers

math.GT2023

Covering radius of RM(4,8)

Valérie Gillot, Philippe Langevin

We propose an effective version of the lift by derivation, an invariant that allows us to provide the classification of B(5,6,8)=RM(6, 8)/RM(4,8). The main consequence is to establ…

cs.DM2022

Classification of some cosets of Reed-Muller codes

Valérie Gillot, Philippe Langevin

This note presents a descending method that allows us to classify quotients of Reed-Muller codes of lenghth 128 under the action of the affine general linear group.

math.NT2016

The $p$ -Adic Valuations of Weil Sums of Binomials

Daniel J. Katz, Philippe Langevin, Sangman Lee +1

We investigate the $p$ -adic valuation of Weil sums of the form $W_{F, d} (a) = \sum_{x \in F} ψ (x^{d} - a x)$ , where $F$ is a finite field of characteristic $p$ , $ψ$ is the canonical addi…

math.NT2014

New Open Problems Related to Old Conjectures by Helleseth

Daniel J. Katz, Philippe Langevin

Recently, very interesting results have been obtained concerning the Fourier spectra of power permutations over a finite field. In this note we survey the recent ideas of Aubry, Fe…

math.NT2014

Proof of a Conjectured Three-Valued Family of Weil Sums of Binomials

Daniel J. Katz, Philippe Langevin

We consider Weil sums of binomials of the form $W_{F, d} (a) = \sum_{x \in F} ψ (x^{d} - a x)$ , where $F$ is a finite field, $ψ : F \to C$ is the canonical additive character,…

math.NT2013

Cyclotomy of Weil Sums of Binomials

Yves Aubry, Daniel J. Katz, Philippe Langevin

The Weil sum $W_{K, d} (a) = \sum_{x \in K} ψ (x^{d} + a x)$ where $K$ is a finite field, $ψ$ is an additive character of $K$ , $d$ is coprime to $∣ K^{\times} ∣$ , and $a \in K^{\times}$ arises…

math.NT2012

On a conjecture of Helleseth

Yves Aubry, Philippe Langevin

We are concern about a conjecture proposed in the middle of the seventies by Hellesseth in the framework of maximal sequences and theirs cross-correlations. The conjecture claims t…