Rocco Trombetti

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We construct six new infinite families of finite semifields, all of which are two-dimensional over their left nuclei. We give constructions for both even and odd characteristics when the left nucleus has odd dimension over the center. The characteristic is odd in the one family in which the left nucleus has even dimension over the center. Spread sets of(More)
For each rank metric code C ⊆ K m×n , 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(More)
There are lovely connections between certain characteristic 2 semi-fields and their associated translation planes and orthogonal spreads on the one hand, and Z 4 –linear Kerdock and Preparata codes on the other. These inter– relationships lead to the construction of large numbers of objects of each type. In the geometric context we construct and study large(More)