On the tensor rank of multiplication in any extension of $\F_2$

Stéphane Ballet (1) , Julia Pieltant (1)

1 IML - Institut de mathématiques de Luminy

In this paper, we obtain new bounds for the tensor rank of multiplication in any extension of $\F_2$. In particular, it also enables us to obtain the best known asymptotic bound. To this aim, we use the generalized algorithm of type Chudnovsky with derivative evaluations on places of degree one, two and four applied on the descent over $\F_2$ of a Garcia-Stichtenoth tower of algebraic function fields defined over $\F_{2^4}$.

Mots clés: Algebraic function fields; tower of function fields; tensor rank; algorithm; finite fields

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]; Complexité [cs.CC]

Stéphane Ballet, Julia Pieltant. On the tensor rank of multiplication in any extension of $\F_2$. Journal of Complexity, 2011, 27 (2), pp.230-245. ⟨10.1016/j.jco.2011.01.008⟩. ⟨hal-00828053⟩