6 papers
A -analogue of the rational normal curve and linearized Reed-Solomon codes
Valentina Astore, Martino Borello, Alain Couvreur +1
The relationship between linear codes in the Hamming metric and projective algebraic varieties has led to deep interactions between coding theory and algebraic geometry, with class…
Maximal quadrics over finite fields and minimal codewords of projective Reed-Muller codes
Alain Couvreur, Rati Ludhani
We study the classification of minimal codewords of projective Reed-Muller codes of order . This problem is equivalent to identifying quadrics over finite fields whose set of ra…
Decoding Algorithms for Tensor Codes
Eimear Byrne, Alain Couvreur, Lucien François
Tensor codes are a generalisation of matrix codes. Such codes are defined as subspaces of order-r tensors for which the ambient space is endowed with the tensor-rank as a metric. A…
Highway to Hull: An Algorithm for Solving the General Matrix Code Equivalence Problem
Alain Couvreur, Christophe Levrat
The matrix code equivalence problem consists, given two matrix spaces of dimension , in finding invertible matrices $P…
MinRank Gabidulin encryption scheme on matrix codes
Nicolas Aragon, Alain Couvreur, Victor Dyseryn +2
The McEliece scheme is a generic frame which allows to use any error correcting code of which there exists an efficient decoding algorithm to design an encryption scheme by hiding…
Freiman's Theorem for Function Fields
Alain Couvreur, Gilles Zémor
Freiman's Theorem states that if a subset of integers has a Minkowski sum of size at most , then it must be contained in a short arithmetic progression.…