Generalised Veroneseans

TL;DR

This paper extends the theory of regular generalised dual arcs, which are used to construct secret sharing schemes, by providing an extension result for these geometric structures.

Contribution

It introduces an extension theorem for regular generalised dual arcs, expanding their theoretical framework and potential applications in cryptography.

Findings

Extension result for regular generalised dual arcs

Application of dual arcs in secret sharing schemes

Enhanced understanding of tangent space properties in finite quadrics

Abstract

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.