On Generalized Steiner Systems and Semi-biplanes

Split Semi-Biplanes in Antiregular Generalized Quadrangles

There are a number of important substructures associated with sets of points of antiregular quadrangles. Inspired by a construction of P. Wild, we associate with any four distinct collinear points p, q, r and s of an antiregular quadrangle an incidence structure which is the union of the two biaffine planes associated with {p, r} and {q, s}. We investigate when this incidence structure is a sem...

Generalized Steiner Systems

Generalized Steiner systems GSd…t; k; v; g† were ®rst introduced by Etzion and used to construct optimal constant-weight codes over an alphabet of size g‡ 1 with minimum Hamming distance d, in which each codeword has length v and weight k. Much work has been done for the existence of generalized Steiner triple systems GS…2; 3; v; g†. However, for block size four there is not much known on GSd…2...

Semi-Boolean Steiner quadruple systems and dimensional dual hyperovals

A dimensional dual hyperoval satisfying property (H) [6] in a project!ve space of order 2 is naturally associated with a "semi-Boolean" Steiner quadruple system. The only known examples are associated with Boolean systems. For every d > 2, we construct a new ddimensional dual hyperoval satisfying property (H) in PG(d(d + 3)/2,2); its related semiBoolean system is the Teirlinck one. It is univer...

Generalized Steiner systems GS5(2, 5, v, 5)

Constructions for generalized Steiner systems GS (3, 4, v , 2)

Generalized Steiner systems GS (3, 4, v, 2) were first discussed by Etzion and used to construct optimal constant weight codes over an alphabet of size three with minimum Hamming distance three, in which each codeword has length v and weight four. Not much is known for GS (3, 4, v, 2)s except for a recursive construction and two small designs for v = 8, 10 given by Etzion. In this paper, more s...