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pro vyhledávání: '"Langevin, Philippe"'
In the BFA 2023 conference paper, A. Polujan, L. Mariot and S. Picek exhibited the first example of a non-normal but weakly normal bent function in dimension 8. In this note, we present numerical approaches based on the classification of Boolean spac
Externí odkaz:
http://arxiv.org/abs/2407.14038
Autor:
Gillot, Valérie, Langevin, Philippe
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 establish that the covering radius of the Reed-Muller RM(4,8) is equal to 26
Externí odkaz:
http://arxiv.org/abs/2305.03493
Autor:
Gillot, Valérie, Langevin, Philippe
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.
Externí odkaz:
http://arxiv.org/abs/2208.02469
We investigate the $p$-adic valuation of Weil sums of the form $W_{F,d}(a)=\sum_{x \in F} \psi(x^d -a x)$, where $F$ is a finite field of characteristic $p$, $\psi$ is the canonical additive character of $F$, the exponent $d$ is relatively prime to $
Externí odkaz:
http://arxiv.org/abs/1608.04047
Autor:
Katz, Daniel J., Langevin, Philippe
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, Feng, Katz, and Langevin, and we pose new open problems related to old c
Externí odkaz:
http://arxiv.org/abs/1412.8530
Autor:
Katz, Daniel J., Langevin, Philippe
We consider Weil sums of binomials of the form $W_{F,d}(a)=\sum_{x \in F} \psi(x^d-a x)$, where $F$ is a finite field, $\psi\colon F\to {\mathbb C}$ is the canonical additive character, $\gcd(d,|F^\times|)=1$, and $a \in F^\times$. If we fix $F$ and
Externí odkaz:
http://arxiv.org/abs/1409.2459
The Weil sum $W_{K,d}(a)=\sum_{x \in K} \psi(x^d + a x)$ where $K$ is a finite field, $\psi$ is an additive character of $K$, $d$ is coprime to $|K^\times|$, and $a \in K^\times$ arises often in number-theoretic calculations, and in applications to f
Externí odkaz:
http://arxiv.org/abs/1312.3889
Autor:
Langevin, Philippe, Wood, Jay A.
Publikováno v:
In Journal of Pure and Applied Algebra March 2019 223(3):922-930
Autor:
Aubry, Yves, Langevin, Philippe
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 the existence of a zero outphase Fourier coefficient. We give some divi
Externí odkaz:
http://arxiv.org/abs/1212.6553
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