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arXiv · 1305.5166

New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields

Julia Pieltant·Hugues Randriam
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Abstract

We obtain new uniform upper bounds for the (non necessarily symmetric) tensor rank of the multiplication in the extensions of the finite fields $\F_q$ for any prime or prime power $q\geq2$; 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.

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Julia Pieltant, Hugues Randriam. 2013-05-22. New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields. https://doi.org/10.1090/s0025-5718-2015-02921-4

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