Optimal Karatsuba-like formulae for certain bilinear forms in GF(2)

We propose two exhaustive search-type methods for the construction of Karatsuba-like algorithms for fast computation of certain bilinear forms in GF(2). The computation is done via an explicit construction of trilinear decompositions using heuristica search algorithms. Using that approach several old and new algorithms for the fast computation of bilinear forms were obtained.