摘要

We obtain new uniform upper bounds for the tensor rank of the multiplication in the extensions of the finite fields F-q for any prime power q; moreover, these uniform bounds lead to new asymptotic bounds as well. In addition, we also give purely asymptotic bounds which are substantially better by using a family of Shimura curves defined over F-q, with an optimal ratio of F(q)t-rational places to their genus, where q(t) is a square.

  • 出版日期2015-7
  • 单位TELECOM ParisTech; INRIA