Classification of 64-element finite semifields

Abstract

A finite semifield $D$ is a finite nonassociative ring with identity such that the set $D^{\ast }=D\setminus \{0\}$ is closed under the product. In this paper we obtain a computer-assisted description of all 64-element finite semifields, which completes the classification of finite semifields of order 125 or less.

25 pages (1 appendix)