13 citations · 19 across the 3 of their papers we have counts for
11 papers
On Codes and Learning With Errors over Function Fields
Maxime Bombar, Alain Couvreur, Thomas Debris-Alazard
It is a long standing open problem to find search to decision reductions for structured versions of the decoding problem of linear codes. Such results in the lattice-based setting…
On the hardness of code equivalence problems in rank metric
Alain Couvreur, Thomas Debris-Alazard, Philippe Gaborit
In the recent years, the notion of rank metric in the context of coding theory has known many interesting developments in terms of applications such as space time coding, network c…
Algebraic geometry codes and some applications
Alain Couvreur, Hugues Randriambololona
This article surveys the development of the theory of algebraic geometry codes since their discovery in the late 70's. We summarize the major results on various problems such as: a…
Rank-metric codes over arbitrary Galois extensions and rank analogues of Reed-Muller codes
Daniel Augot, Alain Couvreur, Julien Lavauzelle +1
This paper extends the study of rank-metric codes in extension fields equipped with an arbitrary Galois group . We propose a f…
Toward good families of codes from towers of surfaces
Alain Couvreur, Philippe Lebacque, Marc Perret
We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and tu…
Power Error Locating Pairs
Alain Couvreur, Isabella Panaccione
We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed--Solomon or algebraic…