Classification of 8-dimensional rank two commutative semifields
Lavrauw, Michel and Rodgers, Morgan (2019) Classification of 8-dimensional rank two commutative semifields. Advances in Geometry, 19 (1). pp. 57-64. ISSN 1615-715X (Print) 1615-7168 (Online)
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Official URL: http://dx.doi.org/10.1515/advgeom-2017-0064
We classify the rank two commutative semifields which are 8-dimensional over their center F-q. This is done using computational methods utilizing the connection to linear sets in PG(2, q(4)). We then apply our methods to complete the classification of rank two commutative semi fields which are 10-dimensional over F-3. The implications of these results are detailed for other geometric structures such as semifield flocks, ovoids of parabolic quadrics, and eggs.
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