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Algebraic Coding and Cryptography
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ACCESS is a joint effort designed to highlight world-class research in coding theory, cryptography, and related areas and to encourage collaboration among its participants.
ACCESS is a joint effort designed to highlight world-class research in coding theory, cryptography, and related areas and to encourage collaboration among its participants.
Next seminar
November 18
Next seminar
November 18
Gilles Zémor
Bordeaux University
Gilles Zémor
Bordeaux University
Schur products of codes, an additive combinatorics perspective
Schur products of codes, an additive combinatorics perspective
Abstract. Schur (or Hadamard) products of codes have a wide variety of applications. Notably, they lead to efficient algebraic decoding algorithms and are behind multiplicative secret-sharing schemes. For most of their applications, one requires pairs of codes whose products have an unusually small dimension. Investigating which pairs of codes have this property conjures striking similarities with questions explored in Additive Combinatorics, notably characterising pairs of sets of integers which sum to a sumset of small cardinality. We shall survey some of these connections, give some results, and discuss a recent application to characterising divisible set families.
Biography. Gilles Zémor has been a professor at the Mathematics Institute of Bordeaux University since 2006. He obtained his PhD in 1989 from Ecole Nationale Supérieure des Télécommunications in Paris. Throughout his career he has been interested in most aspects of Coding Theory, as well as interplay between Coding and other fields, notably Cryptography. He has also regularly been interested in problems from Additive Combinatorics. For the last 15 years he has had a strong interest in the design of quantum LDPC codes.
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