On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry

2019/06/18 by Stéphane Ballet, Ballet, Stéphane, Jean Chaumine +9
Computer Science · Mathematics · #Coding theory and cryptography #Cryptography and Residue Arithmetic #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1906.07456

Abstract

In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite extensions of finite fields, enriched with some not published recent results as well as analyzes enhancing the qualitative understanding of the domain. In particular, we identify and clarify certain results not completely proved and we emphasis the link with open problems in number theory, algebraic geometry, and coding theory.

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