New advances in the computational exploration of semifields (CMMSE-09)

Ignacio Fernandez Rua (1) , Elías Fernandez-Combarro (1) , José Ranilla (1)

1 Universidad de Oviedo [Oviedo]

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 coding theory, combinatorics and graph theory have broaden 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.

Mots clés: Physical Sciences

Domaines: Informatique [cs]

Ignacio Fernandez Rua, Elías Fernandez-Combarro, José Ranilla. New advances in the computational exploration of semifields (CMMSE-09). International Journal of Computer Mathematics, 2011, 88 (09), pp.1988-1998. ⟨10.1080/00207160.2010.548518⟩. ⟨hal-00687736⟩