1 citations · 1 across the 9 of their papers we have counts for
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Symplectic 4-dimensional semifields of order and
Michel Lavrauw, John Sheekey
We classify symplectic 4-dimensional semifields over , for , thereby extending (and confirming) the previously obtained classifications for . The cl…
Rank-Metric Codes, Semifields, and the Average Critical Problem
Anina Gruica, Alberto Ravagnani, John Sheekey +1
We investigate two fundamental questions intersecting coding theory and combinatorial geometry, with emphasis on their connections. These are the problem of computing the asymptoti…
The Tensor Rank of Semifields of Order 16 and 81
Michel Lavrauw, John Sheekey
We determine the tensor rank of all semifields of order 16 over and of all semifields of order 81 over . Our results imply that some semifields of orde…
Combinatorial invariants for nets of conics in
Michel Lavrauw, Tomasz Popiel, John Sheekey
The problem of classifying linear systems of conics in projective planes dates back at least to Jordan, who classified pencils (one-dimensional systems) of conics over …
Nets of conics of rank one in PG(2,q), q odd
Michel Lavrauw, Tomasz Popiel, John Sheekey
We classify nets of conics in Desarguesian projective planes over finite fields of odd order, namely, two-dimensional linear systems of conics containing a repeated line. Our proof…
On the product of elements with prescribed trace
John Sheekey, José Felipe Voloch, Geertrui Van de Voorde
This paper deals with the following problem. Given a finite extension of fields and denoting the trace map from to by $\mathrm{Tr}…