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## 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 $\left({X}^{5}-1\right)$. Moreover, we prove that there is essentially only one optimal decomposition of the product of $3×2$ by $2×3$ matrices up to the action of some group of automorphisms.