## Section: New Results

### Improved Methods for Finding Optimal Formulae for Bilinear Maps in a Finite Field

Participant : Svyatoslav Covanov.

In [17], we describe a method improving on the exhaustive search algorithm developed in [26]. We are able to compute new optimal formulae for the short product modulo ${X}^{5}$ and the circulant product modulo $({X}^{5}-1)$. Moreover, we prove that there is essentially only one optimal decomposition of the product of $3\times 2$ by $2\times 3$ matrices up to the action of some group of automorphisms.