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

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

2010-03-09

arxiv.org/abs/1003.1864v1

Mathematics

Algebraic Geometry

Scientific paper

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. In 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 $\F_{2^4}$.

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