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We propose several constructions for the original multiplication algorithm of D.V. and G.V. Chudnovsky in order to improve its scalar complexity. We highlight the set of generic strategies who underlay the optimization of the scalar complexity, according to parameterizable criteria. As an example, we apply this analysis to the construction of type elliptic Chudnovsky$^2$ multiplication algorithms for small extensions. As a case study, we significantly improve the Baum-Shokrollahi construction for multiplication in $mathbb F_{256}/mathbb F_4$.
We propose a Recursive Polynomial Generic Construction (RPGC) of multiplication algorithms in any finite field $mathbb{F}_{q^n}$ based on the method of D.V. and G.V. Chudnovsky specialized on the projective line. They are usual polynomial interpolati
The Chudnovsky and Chudnovsky algorithm for the multiplication in extensions of finite fields provides a bilinear complexity which is uniformly linear whith respect to the degree of the extension. Recently, Randriambololona has generalized the method
We indicate a strategy in order to construct bilinear multiplication algorithms of type Chudnovsky in large extensions of any finite field. In particular, by using the symmetric version of the generalization of Randriambololona specialized on the ell
Thanks to a new construction of the so-called Chudnovsky-Chudnovsky multiplication algorithm, we design efficient algorithms for both the exponentiation and the multiplication in finite fields. They are tailored to hardware implementation and they al
We present three families of minimal border rank tensors: they come from highest weight vectors, smoothable algebras, or monomial algebras. We analyse them using Strassens laser method and obtain an upper bound $2.431$ on $omega$. We also explain how