Rocco Trombetti

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In this paper we prove that the projections along reguli of a translation spread of the classical generalized hexagon H(q) are translation ovoids of Q(4, q). As translation ovoids of Q(4, 2r ) are elliptic quadrics, this forces that all translation spreads of H(2r ) are semi-classical. By representing H(q) as a coset geometry, we obtain a characterization(More)
A new construction is given of cyclic semifields of orders q2n, n odd, with kernel (left nucleus) Fqn and right and middle nuclei isomorphic to Fq2 , and the isotopism classes are determined. Furthermore, this construction is generalized to produce potentially new semifields of the same general type that are not isotopic to cyclic semifields. In particular,(More)
For each rank metric code C ⊆ K, we associate a translation structure, the kernel of which is showed to be invariant with respect to the equivalence on rank metric codes. When C is K-linear, we also propose and investigate other two invariants called its middle nucleus and right nucleus. When K is a finite field Fq and C is a maximum rank distance code with(More)