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Journal articles
New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields
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.
Cited literature [21 references]
https://hal.archives-ouvertes.fr/hal-00828153
Contributor : Julia Pieltant Connect in order to contact the contributor
Submitted on : Friday, May 31, 2013 - 11:17:19 AM
Last modification on : Monday, January 24, 2022 - 11:43:20 AM
Long-term archiving on: : Tuesday, April 4, 2017 - 1:47:53 PM
Contributor : Julia Pieltant Connect in order to contact the contributor
Submitted on : Friday, May 31, 2013 - 11:17:19 AM
Last modification on : Monday, January 24, 2022 - 11:43:20 AM
Long-term archiving on: : Tuesday, April 4, 2017 - 1:47:53 PM
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