The FBHHRBNRSSSHK-Algorithm for Multiplication in $\mathbb{Z}_2^{5\times5}$ is still not the end of the story

TL;DR

This paper introduces a new algorithm for multiplying 5x5 matrices over _2 that reduces the number of multiplications from 96 to 95, improving upon the previous best record.

Contribution

The paper presents a novel algorithm for 5x5 matrix multiplication over _2 requiring fewer multiplications than the prior record.

Findings

Achieved 95 multiplications for 5x5 matrix multiplication over _2

Improved the previous record of 96 multiplications

Contributes to the ongoing effort to optimize matrix multiplication algorithms

Abstract

In response to a recent Nature article which announced an algorithm for multiplying $5\times5$-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.