82
Views
12
CrossRef citations to date
0
Altmetric
Section B

New advances in the computational exploration of semifields

, &
Pages 1990-2000 | Received 01 Nov 2009, Accepted 18 Nov 2010, Published online: 14 Apr 2011
 

Abstract

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.

2010 AMS Subject Classifications :

Acknowledgements

The authors thankfully acknowledge the computer resources, technical expertise and assistance provided by the Centro de Supercomputación y Visualización de Madrid (CeSViMa) and the Spanish Supercomputing Network. E.F. Combarro and J. Ranilla are partially supported by MICINN-TIN2010-14971, MEC-TIN2007-61273 and MEC-TIN2007-29664E and I.F. Rúa is partially supported by MEC-MTM-2010-18370-C04-01, MEC-MTM2007-67884 C04-01 and IB08-147.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.