Towards a function field version of Freiman's Theorem
COUVREUR, Alain
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
COUVREUR, Alain
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
< Reduce
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
Language
en
Article de revue
This item was published in
Algebraic Combinatorics. 2018, vol. 1, n° 4, p. 501-521
MathOA
English Abstract
We discuss a multiplicative counterpart of Freiman's 3k−4 theorem in the context of a function field F over an algebraically closed field K. Such a theorem would give a precise description of subspaces S, such that the ...Read more >
We discuss a multiplicative counterpart of Freiman's 3k−4 theorem in the context of a function field F over an algebraically closed field K. Such a theorem would give a precise description of subspaces S, such that the space S^2 spanned by products of elements of S satisfies dim S^ 2 ≤ 3 dimS − 4. We make a step in this direction by giving a complete characterisation of spaces S such that dimS^2 = 2 dimS. We show that, up to multiplication by a constant field element, such a space S is included in a function field of genus 0 or 1. In particular if the genus is 1 then this space is a Riemann-Roch space.Read less <
ANR Project
Geométrie algébrique et théorie des codes pour la cryptographie - ANR-15-CE39-0013
Origin
Hal imported