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Article Dans Une Revue Mathematics of Computation Année : 2015

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

Résumé

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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