New advances in the computational exploration of semifields

作者：Combarro Elias F; Rua I F; Ranilla J^*

来源：International Journal of Computer Mathematics, 2011, 88(9): 1990-2000.

DOI：10.1080/00207160.2010.548518

• finite semifield
• finite division ring
• computational methods
• classification
• primitivity

Finite semifields (finite non-necessarily associative division rings) have traditionally been considered in the context of finite geometries (they coordinatize projective semifield planes). New applications to the coding theory, combinatorics and the graph theory have broadened the potential interest in these rings. We show recent progress in the study of these objects with the help of computational tools. In particular, we state results on the classification and primitivity of semifields obtained with the help of advanced and efficient implementations (both sequential and parallel) of different algorithms specially designed to manipulate these objects.

• 出版日期2011