90 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Laboratoire d'Informatique de l'École PolytechniqueFR10 papers
- Centre Inria de SaclayFR9 papers
- École PolytechniqueFR9 papers
- Institut national de recherche en sciences et technologies du numériqueFR7 papers
- Centre National de la Recherche ScientifiqueFR6 papers
- Aix-Marseille UniversitéFR2 papers
- Différenciation et Communication Neuronale et NeuroendocrineFR2 papers
- Institut de Mathématiques de MarseilleFR2 papers
- Laboratoire d'Informatique, du Traitement de l'Information et des SystèmesFR2 papers
- Normandie UniversitéFR2 papers
- Université Paris-SaclayFR2 papers
- Boğaziçi UniversityTR1 paper
11 papers
How arithmetic and geometry make error correcting codes better
Alain Couvreur
This note completes a talk given at the conference Curves over Finite Fields: past, present and future celebrating the publication the book {\em Rational Points on Curves over Fini…
Lifted Projective Reed-Solomon Codes
Julien Lavauzelle
Lifted Reed-Solomon codes, introduced by Guo, Kopparty and Sudan in 2013, are known as one of the few families of high-rate locally correctable codes. They are built through the ev…
Private Information Retrieval from Transversal Designs
Julien Lavauzelle
Private information retrieval (PIR) protocols allow a user to retrieve entries of a database without revealing the index of the desired item. Information-theoretical privacy can be…
Remarks on Tsfasman-Boguslavsky Conjecture and Higher Weights of Projective Reed-Muller Codes
Mrinmoy Datta, Sudhir R. Ghorpade
Tsfasman-Boguslavsky Conjecture predicts the maximum number of zeros that a system of linearly independent homogeneous polynomials of the same positive degree with coefficients in…
Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes
Ping Ngai Chung, Craig Costello, Benjamin Smith
We give a general framework for uniform, constant-time one-and two-dimensional scalar multiplication algorithms for elliptic curves and Jacobians of genus 2 curves that operate by…
New Identities Relating Wild Goppa Codes
Alain Couvreur, Ayoub Otmani, Jean-Pierre Tillich
For a given support and a polynomial with no roots in , we prove equality between the -ary Goppa codes $Γ…
Decoding color codes by projection onto surface codes
Nicolas Delfosse
We propose a new strategy to decode color codes, which is based on the projection of the error onto three surface codes. This provides a method to transform every decoding algorith…
Distinguisher-Based Attacks on Public-Key Cryptosystems Using Reed-Solomon Codes
Alain Couvreur, Philippe Gaborit, Valérie Gauthier-Umaña +2
Because of their interesting algebraic properties, several authors promote the use of generalized Reed-Solomon codes in cryptography. Niederreiter was the first to suggest an insta…
Shimura modular curves and asymptotic symmetric tensor rank of multiplication in any finite field
Stéphane Ballet, Jean Chaumine, Julia Pieltant
We obtain new asymptotical bounds for the symmetric tensor rank of multiplication in any finite extension of any finite field $\F_q$. In this aim, we use the symmetric Chudnovsky-t…
New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields
Julia Pieltant, Hugues Randriam
We obtain new uniform upper bounds for the (non necessarily symmetric) tensor rank of the multiplication in the extensions of the finite fields $\F_q$ for any prime or prime power…
Computing coset leaders and leader codewords of binary codes
M. Borges-Quintana, M. A. Borges-Trenard, I. Márquez-Corbella +1
In this paper we use the Gröbner representation of a binary linear code to give efficient algorithms for computing the whole set of coset leaders, denoted by $\mathrm{…