On the tensor rank of multiplication in any extension of

Abstract: In this paper, we obtain new bounds for the tensor rank of multiplication in any extension of . 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 of a Garcia–Stichtenoth tower of algebraic function fields defined over . [Copyright &y& Elsevier]