29 citations · 46 across the 11 of their papers we have counts for
13 papers
The syzygy distinguisher
Hugues Randriambololona
We present a new distinguisher for alternant and Goppa codes, whose complexity is subexponential in the error-correcting capability, hence better than that of generic decoding algo…
Algebraic geometry codes and some applications
Alain Couvreur, Hugues Randriambololona
This article surveys the development of the theory of algebraic geometry codes since their discovery in the late 70's. We summarize the major results on various problems such as: a…
The quadratic hull of a code and the geometric view on multiplication algorithms
Hugues Randriambololona
We introduce the notion of quadratic hull of a linear code, and give some of its properties. We then show that any symmetric bilinear multiplication algorithm for a finite-dimensio…
On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry
Stéphane Ballet, Jean Chaumine, Julia Pieltant +3
In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite extensions of finite fields, enriched with some not published recent…
On metric convexity, the discrete Hahn-Banach theorem, separating systems and sets of points forming only acute angles
Hugues Randriambololona
This text has three parts. The first one is largely autobiographical, hence my use of the first person. There I recall how Gerard Cohen influenced important parts of my research. T…
Harder-Narasimhan theory for linear codes
Hugues Randriambololona
In this text we develop some aspects of Harder-Narasimhan theory, slopes, semistability and canonical filtration, in the setting of combinatorial lattices. Of noticeable importance…
Linear independence of rank 1 matrices and the dimension of *-products of codes
Hugues Randriambololona
We show that with high probability, random rank 1 matrices over a finite field are in (linearly) general position, at least provided their shape k x l is not excessively unbalanced…
On products and powers of linear codes under componentwise multiplication
Hugues Randriambololona
In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is pu…
An upper bound of Singleton type for componentwise products of linear codes
Hugues Randriambololona
We give an upper bound that relates the minimum weight of a nonzero componentwise product of codewords from some given number of linear codes, with the dimensions of these codes. I…
Asymptotically good binary linear codes with asymptotically good self-intersection spans
Hugues Randriambololona
If C is a binary linear code, let C^2 be the linear code spanned by intersections of pairs of codewords of C. We construct an asymptotically good family of binary linear codes such…
On the tensor rank of multiplication in finite extensions of finite fields
Stéphane Ballet, Jean Chaumine, Julia Pieltant +1
In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite fields and we establish new asymptotical and not asymptotical upper…
Bilinear complexity of algebras and the Chudnovsky-Chudnovsky interpolation method
Hugues Randriambololona
We give new improvements to the Chudnovsky-Chudnovsky method that provides upper bounds on the bilinear complexity of multiplication in extensions of finite fields through interpol…
(2,1)-separating systems beyond the probabilistic bound
Hugues Randriambololona
Building on previous results of Xing, we give new lower bounds on the rate of intersecting codes over large alphabets. The proof is constructive, and uses algebraic geometry, altho…