Steiner systems for two-stage disjunctive testing

The subject of this paper are some constructions of Steiner designs with blocks of two sizes that differ by one. The study of such designs is motivated by a combinatorial lower bound on the minimum number of individual tests at the second stage of a 2-stage disjunctive testing algorithm.     

On block designs arising from rank 3 graphs

In this paper a criterion showing when the orbit of a subgraph of a given rank 3 graph forms a block design, is given. As an application several classes of block designs are derived from the triangular graph T(n) and the lattice graph L₂(n).     

Cyclic quasi-symmetric designs and self-orthogonal codes of length 63

The enumeration of binary cyclic self-orthogonal codes of length 63 is used to prove that any cyclic quasi-symmetric 2-(63,15,35)$2\text{-}(63,15,35)$ design with block intersection numbers x=3$x=3$ and y=7$y=7$ is isomorphic to the geometric design having as blocks the three-dimensional subspaces in PG(5,2)$\text{<italic>PG</italic>}(5,2)$.     

An algorithm for optimal difference systems of sets

Difference Systems of Sets (DSS) are combinatorial structures that generalize cyclic difference sets and are used in code synchronization. A DSS is optimal if the associated code has minimum redundancy for the given block length n, alphabet size q, and error-correcting capacity ρ. An algorithm for finding optimal DSS is presented together with tables of optimal solutions found by this algorithm. Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday. Research supported by NSF Grant CCR-0310632.