In this note we offer a short summary of some recent results, to be contained in a forthcoming paper [4], on projective caps and linear error correcting codes arising from the Grassmann embedding ε k of an orthogonal Grassmannian ∆k. More precisely, we consider the codes arising from the projective system determined by ε k (∆k) and determine some of their parameters. We also investigate special...

In this paper we deal with the special class of covering codes consisting of multiple coverings of the farthest-off points (MCF). In order to measure the quality of an MCF code, we use a natural extension of the notion of density for ordinary covering codes, that is the μ-density for MCF codes; a generalization of the length function for linear covering codes is also introduced. Our main result...

The Platonic graphs πn arise in several contexts, most simply as a quotient of certain Cayley graphs associated to the projective special linear groups. We show that when n = p is prime, πn can be viewed as a complete multigraph in which each vertex is itself a wheel on n + 1 vertices. We prove a similar structure theorem for the case of an arbitrary prime power. These theorems are then used to...

Let X ⊂ P be an n-dimensional connected projective submanifold of projective space. Let p : P → P denote the projection from a linear P ⊂ P . Assuming that X 6⊂ P we have the induced rational mapping ψ := pX : X → P. This article started as an attempt to understand the structure of this mapping when ψ has a lower dimensional image. In this case of necessity we have Y := X ∩ P is nonempty. The s...

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