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Journal Articles Mathematics of Computation Year : 2015

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

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Abstract

We obtain new uniform upper bounds for the tensor rank of the multiplication in the extensions of the finite fields $\mathbb{F}_q$ 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 $\mathbb{F}_q$, with an optimal ratio of $\mathbb{F}_{q^t}$-rational places to their genus, where $q^t$ is a square.
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hal-00828153 , version 1 (31-05-2013)

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Julia Pieltant, Hugues Randriambololona. New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields. Mathematics of Computation, 2015, 84 (294), pp.2023-2045. ⟨10.1090/S0025-5718-2015-02921-4⟩. ⟨hal-00828153⟩
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