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Bibliographic Details
Main Authors: Ballet, Stéphane, Rolland, Robert
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.12383
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Table of Contents:
  • We design a class of Chudnovsky-type algorithms multiplying k elements of a finite extension of order n a finite field K. We prove that these algorithms give a tensor decomposition of the k-multiplication for which the rank is linear in n uniformly in $q$. We give uniform upper bounds of the rank of k-multiplication in finite fields. They use interpolation on algebraic curves which transforms the problem in computing the Hadamard product of $k$ vectors with components in K. This generalization of the widely studied case of $k=2$ is based on a modification of the Riemann-Roch spaces involved and the use of towers of function fields having a lot of places of high degree.