Section: New Results

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

Participant : Svyatoslav Covanov.

In [15], we described a method improving on the exhaustive search algorithm originally developed in  [19]. 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 proved 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. This work has been submitted to Theoretical Computer Science and is tentatively accepted, pending minor revisions.