This is an expository article detailing results concerning large arcs in finite projective spaces.
It is not strictly a survey but attempts to cover the most relevant results on arcs, simplifying …

In this paper, we propose a new secure distributed matrix multiplication (SDMM) scheme
using the inner product partitioning. We construct a scheme with a minimal number of …

A normal rational curve of the (k-1)-dimensional projective space over Fq is an arc of size q+
1, since any k points of the curve span the whole space. In this paper, we will prove that if q …

A map that is defined on the set of all symmetric matrices over a field is rank-one
nonincreasing if it maps the matrices of rank one to matrices of rank at most one. In the case …

An arc is a set of vectors of the k-dimensional vector space over the finite field with q
elements F _q F q, in which every subset of size k is a basis of the space, ie every k-subset is …

Abstract—In the projective plane PG (2, q), a subset S of a conic C is said to be almost
complete if it can be extended to a larger arc in PG (2, q) only by the points of C\S and by the …

An arc is a set of points of the (k-1)-dimensional projective space over the finite field with q
elements\mathbb F _q, in which every k-subset spans the space. In this article, we firstly …

Новые границы используются для увеличения мощности множества пар (N, q), для
которых доказано, что каждая нормальная рациональная кривая в проективном …

A subset $\mathcal {S} $ of a conic $\mathcal {C} $ in the projective plane $\mathrm {PG}(2,
q) $ is called almost complete (AC-subset for short) if it can be extended to a larger arc in …