Generalised Veroneseans

In \cite{ThasHVM}, a characterization of the finite quadric Veronesean ${\mathcal{V}}_n^{2^n}$ by means of properties of the set of its tangent spaces is proved. These tangent spaces form a {\em regular generalised dual arc}. We prove an extension result for regular generalised dual arcs. To motivate our research, we show how they are used to construct a large class of secret sharing schemes.