Polarities, quasi-symmetric designs, and Hamada's conjecture

Finite geometry designs, codes, and Hamada's conjecture

New quasi-symmetric designs by the Kramer-Mesner method

A t-(v, k, λ) design is quasi-symmetric if there are only two block intersection sizes. We adapt the Kramer-Mesner construction method for designs with prescribed automorphism groups to the quasi-symmetric case. Using the adapted method, we find many new quasi-symmetric 2-(28, 12, 11) and 2-(36, 16, 12) designs, establish the existence of quasi-symmetric 2-(56, 16, 18) designs, and find three n...

Pseudo Quasi-3 Designs and their Applications to Coding Theory

We define a pseudo quasi-3 design as a symmetric design with the property that the derived and residual designs with respect to at least one block are quasi-symmetric. Quasi-symmetric designs can be used to construct optimal self complementary codes. In this article we give a construction of an infinite family of pseudo quasi-3 designs whose residual designs allow us to construct a family of co...

Construction of a Class of Quasi-Symmetric 2-Designs

In this article we study proper quasi-symmetric 2 − designs i.e. block designs having two intersection numbers and , where 0 < < . Also, we present a construction method for quasi-symmetric 2 − designs with block intersection numbers and + 1, where is a prime number, under certain conditions on the cardinality of point set.

Quasi-symmetric 3-designs with a fixed block intersection number

Quasi-symmetric 3-designs with block intersection numbers x, y (0 ≤ x ≤ y < k) are studied. It is proved that the parameter λ of a quasi-symmetric 3-(v, k, λ) design satisfies a quadratic whose coefficients are polynomial functions of k, x and y. We use this quadratic to prove that there exist finitely many quasi-symmetric 3-designs under either of the following two restrictions: 1. The block i...