Studying algorithms admitting nontrivial symmetries is a prospective way of constructing new short algorithms of matrix multiplication. The main result of the article is that if there exists an algorithm of multiplicative length $l\leq22$ for multuplication of $3\times3$ matrices then its automorphism group is isomorphic to a subgroup of $S_l\times S_3$.
- Pub Date:
- November 2022
- Computer Science - Computational Complexity;
- Mathematics - Group Theory;
- 68Q25 (Primary);
- 20C99 (Secondary);
- 11 pp. To be submitted to European J. Math