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# Shimura modular curves and asymptotic symmetric tensor rank of multiplication in any finite field

* Corresponding author
4 GRACE - Geometry, arithmetic, algorithms, codes and encryption
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : We obtain new asymptotical bounds for the symmetric tensor rank of multiplication in any finite extension of any finite field~$\F_q$. In this aim, we use the symmetric Chudnovsky-type generalized algorithm applied on a family of Shimura modular curves defined over $\F_{q^2}$ attaining the Drinfeld-Vl\u{a}du\c{t} bound and on the descent of this family over the definition field $\F_q$.
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Cited literature [24 references]

https://hal.archives-ouvertes.fr/hal-00828070
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Submitted on : Friday, May 31, 2013 - 11:19:45 AM
Last modification on : Saturday, June 25, 2022 - 7:44:39 PM
Long-term archiving on: : Tuesday, April 4, 2017 - 1:44:15 PM

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### Citation

Stéphane Ballet, Jean Chaumine, Julia Pieltant. Shimura modular curves and asymptotic symmetric tensor rank of multiplication in any finite field. Conference on Algebraic Informatics, Sep 2013, Porquerolles Island, France. pp.160-172, ⟨10.1007/978-3-642-40663-8_16⟩. ⟨hal-00828070⟩

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