287 citations · 1.1k across the 48 of their papers we have counts for
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On the dimension and structure of the square of the dual of a Goppa code
Rocco Mora, Jean-Pierre Tillich
The Goppa Code Distinguishing (GD) problem asks to distinguish efficiently a generator matrix of a Goppa code from a randomly drawn one. We revisit a distinguisher for alternant an…
Quantum Reduction of Finding Short Code Vectors to the Decoding Problem
Thomas Debris-Alazard, Maxime Remaud, Jean-Pierre Tillich
We give a quantum reduction from finding short codewords in a random linear code to decoding for the Hamming metric. This is the first time such a reduction (classical or quantum)…
Decoding Reed-Solomon codes by solving a bilinear system with a Gröbner basis approach
Magali Bardet, Rocco Mora, Jean-Pierre Tillich
Decoding a Reed-Solomon code can be modeled by a bilinear system which can be solved by Gröbner basis techniques. We will show that in this particular case, these techniques are mu…