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

Abstract

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 $\F_{2^4}$.

References in corpus (1)

• On the existence of dimension zero divisors in algebraic function fields defined over F_q

Cited by in corpus (5)

• Squares of Random Linear Codes
• Torsion Limits and Riemann-Roch Systems for Function Fields and Applications
• New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields
• On Chudnovsky-Based Arithmetic Algorithms in Finite Fields
• Bilinear complexity of algebras and the Chudnovsky-Chudnovsky interpolation method