52 citations · 134 across the 30 of their papers we have counts for
13 papers · 1 filter
Improved decoding of symmetric rank metric errors
Alain Couvreur
We consider the decoding of rank metric codes assuming the error matrix is symmetric. We prove two results. First, for rates there exists a broad family of rank metric codes…
Right-hand side decoding of Gabidulin code and applications
Maxime Bombar, Alain Couvreur
We discuss the decoding of Gabidulin and interleaved Gabidulin codes. We give the full presentation of a decoding algorithm for Gabidulin codes, which as Loidreau's seminal algorit…
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…
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…
On the security of a Loidreau's rank metric code based encryption scheme
Daniel Coggia, Alain Couvreur
We present a polynomial time attack of a rank metric code based encryption scheme due to Loidreau for some parameters.
On tensor products of CSS Codes
Benjamin Audoux, Alain Couvreur
CSS codes are in one-to-one correspondance with length 3 chain complexes. The latter are naturally endowed with a tensor product which induces a similar operation on the…
Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes
Alain Couvreur, Irene Márquez-Corbella, Ruud Pellikaan
We give a polynomial time attack on the McEliece public key cryptosystem based on subcodes of algebraic geometry (AG) codes. The proposed attack reposes on the distinguishability o…
Cryptanalysis of McEliece Cryptosystem Based on Algebraic Geometry Codes and their subcodes
Alain Couvreur, Irene Márquez-Corbella, Ruud Pellikaan
We give polynomial time attacks on the McEliece public key cryptosystem based either on algebraic geometry (AG) codes or on small codimensional subcodes of AG codes. These attacks…
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…
Evaluation Codes from smooth Quadric Surfaces and Twisted Segre Varieties
Alain Couvreur, Iwan Duursma
We give the parameters of any evaluation code on a smooth quadric surface. For hyperbolic quadrics the approach uses elementary results on product codes and the parameters of codes…
Incidence structures from the blown-up plane and LDPC codes
Alain Couvreur
In this article, new regular incidence structures are presented. They arise from sets of conics in the affine plane blown-up at its rational points. The LDPC codes given by these i…