In this paper, we give a survey of the known results concerning the tensor rank of
multiplication in finite extensions of finite fields, enriched with some unpublished recent …

Given a linear code C, one can define the dth power of C as the span of all componentwise
products of d elements of C. A power of C may quickly fill the whole space. Our purpose is to …

The Ihara limit (or constant) has been a central problem of study in the asymptotic theory of
global function fields (or equivalently, algebraic curves over finite fields). It addresses global …

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 that …

In this invited talk, 1 we introduce the notion of arithmetic codex, or codex for short. It
encompasses several well-established notions from cryptography (arithmetic secret sharing …

We indicate a strategy in order to construct bilinear multiplication algorithms of type
Chudnovsky in large extensions of any finite field. In particular, using the symmetric version …

We obtain new uniform upper bounds for the tensor rank of the multiplication in the
extensions of the finite fields $\mathbb {F} _q $ for any prime power $ q $; moreover, these …

We establish new upper bounds about symmetric bilinear complexity in any extension of
finite fields. Note that these bounds are not asymptotical but uniform. Moreover we give …

We obtain new asymptotical bounds for the symmetric tensor rank of multiplication in any
finite extension of any finite field F_q. In this aim, we use the symmetric Chudnovsky-type …

In 1999, **ng, Niederreiter and Lam introduced a generalization of AG codes using the
evaluation at non-rational places of a function field. In this paper, we show that one can …