38 citations · 118 across the 16 of their papers we have counts for
7 papers · 1 filter
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…
Generalized Gabidulin codes over fields of any characteristic
Daniel Augot, Pierre Loidreau, Gwezheneg Robert
We generalise Gabidulin codes to the case of infinite fields, eventually with characteristic zero. For this purpose, we consider an abstract field extension and any automorphism in…
Information Sets of Multiplicity Codes
Daniel Augot, Françoise Levy-Dit-Vehel, Man Cuong Ngô
We here provide a method for systematic encoding of the Multiplicity codes introduced by Kopparty, Saraf and Yekhanin in 2011. The construction is built on an idea of Kop-party. We…
Rank metric and Gabidulin codes in characteristic zero
Gwezheneg Robert, Pierre Loidreau, Daniel Augot
We transpose the theory of rank metric and Gabidulin codes to the case of fields of characteristic zero. The Frobenius automorphism is then replaced by any element of the Galois gr…
An Interpolation Procedure for List Decoding Reed--Solomon codes Based on Generalized Key Equations
Alexander Zeh, Christian Gentner, Daniel Augot
The key step of syndrome-based decoding of Reed-Solomon codes up to half the minimum distance is to solve the so-called Key Equation. List decoding algorithms, capable of decoding…
List-decoding of binary Goppa codes up to the binary Johnson bound
Daniel Augot, Morgan Barbier, Alain Couvreur
We study the list-decoding problem of alternant codes, with the notable case of classical Goppa codes. The major consideration here is to take into account the size of the alphabet…