Classification of 64-element finite semifields

Mathematics – Rings and Algebras

Scientific paper

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25 pages (1 appendix)

Scientific paper

A finite semifield $D$ is a finite nonassociative ring with identity such
that the set $D^*=D\setminus\{0\}$ 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.

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