The FBHHRBNRSSSHK-Algorithm for Multiplication in ${\mathbb{Z}}_2^{5\times 5}$ is still not the end of the story

Abstract

In response to a recent Nature article which announced an algorithm for multiplying $5\times 5$-matrices over ${\mathbb{Z}}_2$ with only 96 multiplications, two fewer than the previous record, we present an algorithm that does the job with only 95 multiplications.