Publications (11)
Lower bounds on the minimum distance of long codes in the Lee metric
Hugues Randriam, Lin Sok, Patrick Solé
The Gilbert type bound for codes in the title is reviewed, both for small and large alphabets. Constructive lower bounds better than these existential bounds are derived from geome…
Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faisceaux cohérents
Hugues Randriam
The aim of this paper is twofold. First we prove a theorem of extension of sections of a coherent subquotient of a hermitian vector bundle on a complex analytic space with control…
Witness sets
Gerard Cohen, Hugues Randriam, Gilles Zemor
Given a set C of binary n-tuples and c in C, how many bits of c suffice to distinguish it from the other elements in C? We shed new light on this old combinatorial problem and impr…
Interactive Oracle Proofs of Proximity to Algebraic Geometry Codes
Sarah Bordage, Mathieu Lhotel, Jade Nardi +1
In this work, we initiate the study of proximity testing to Algebraic Geometry (AG) codes. An AG code over an algebraic curve is…
Diviseurs de la forme 2D-G sans sections et rang de la multiplication dans les corps finis (Divisors of the form 2D-G without sections and bilinear complexity of multiplication in finite fields)
Hugues Randriam
Let X be an algebraic curve, defined over a perfect field, and G a divisor on X. If X has sufficiently many points, we show how to construct a divisor D on X such that l(2D-G)=0, o…
Standard Lattices of Compatibly Embedded Finite Fields
Luca De Feo, Hugues Randriam, Ãdouard Rousseau
Lattices of compatibly embedded finite fields are useful in computer algebra systems for managing many extensions of a finite field at once. They can also be used to…