Classification of 64-element finite semifields
I.F. R\'ua, El\'ias F. Combarro, J. Ranilla
TL;DR
This paper provides a comprehensive computer-assisted classification of all 64-element finite semifields, completing the understanding of semifields of order up to 125.
Contribution
It offers the first complete classification of all 64-element finite semifields, expanding the known catalog of small semifields.
Findings
Complete list of 64-element finite semifields
Classification up to order 125 achieved
New structures identified within the classification
Abstract
A finite semifield is a finite nonassociative ring with identity such that the set 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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Taxonomy
TopicsCoding theory and cryptography · Protein Degradation and Inhibitors · Finite Group Theory Research