Sets with few Intersection Numbers from Singer Subgroup Orbits

Sets with few Intersection Numbers from Singer Subgroup Orbits

Using a Singer cycle in Desarguesian planes of order q ≡ 1 (mod 3), q a prime power, Brouwer [2] gave a construction of sets such that every line of the plane meets them in one of three possible intersection sizes. These intersection sizes x, y, and z satisfy the system of equations

t-Designs with few intersection numbers

Pott, A. and M. Shriklande, t-Designs with few intersection numbers, Discrete Mathematics 90 (1991) 215-217. We give a method to obtain new i-designs from t-designs with j distinct intersection numbers if i + j 1 does not exceed t.

On Sets with Few Intersection Numbers in Finite Projective and Affine Spaces

In this paper we study sets X of points of both affine and projective spaces over the Galois field GF(q) such that every line of the geometry that is neither contained in X nor disjoint from X meets the set X in a constant number of points and we determine all such sets. This study has its main motivation in connection with a recent study of neighbour transitive codes in Johnson graphs by Liebl...

Cyclic Orbit Codes with the Normalizer of a Singer Subgroup

An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...

A Note on Intersection Numbers of Difference Sets