We prove that no Suzuki group Sz(q) can act line-transitively on a non-trivial %nite linear space. c © 2002 Elsevier B.V. All rights reserved. MSC: 05B05; 20B25

In this paper some properties of k-chromatic and strong k-chromatic hypergraphs are proved. Conditions for the possible existence of blocking sets in Steiner systems are established. Mathematics Subject Classification: 05C15; 05B05

Let p and 2p − 1 be prime powers and p ≡ 3 (mod 4). Then there exists a symmetric design with parameters (4p, 2p − p, p − p). Thus there exists a regular Hadamard matrix of order 4p. AMS classification numbers: 05B20, 05B05

In this paper, we determine the spectrum (the set of all possible volumes) of simple (v, 3, 2) trades for any fixed foundation size v 6≡ 5 (mod 6). Index Words: trades, spectrum, Steiner triple systems, large sets of Steiner triple systems MR Subject Classification: 05B07, 05B05

Two Hadamard matrices are considered equivalent if one is obtained from the other by a sequence of operations involving row or column permutations or negations. We complete the classification of Hadamard matrices of order 32. It turns out that there are exactly 13710027 such matrices up to equivalence. AMS Subject Classification: 05B20, 05B05, 05B30.

It is shown that in some cases it is possible to reconstruct a block design D uniquely from incomplete knowledge of a minimal defining set for D. This surprising result has implications for the use of minimal defining sets in secret sharing schemes. AMS classifications: Primary: 94A62, Secondary: 05B05.

A 3-gdd of type gu exists if and only if g and u have the same parity, 3 divides u and u ≤ 3g. Such a 3-gdd of type gu is equivalent to an edge decomposition of Kg,g,g,u,u into triangles. 2010 MSC: 05B05, 05B07, 05C70

Many different divisible designs are already known. Some of them possess remarkable automorphism groups, so called dual translation groups. The existence of such an automorphism group enables us to characterize its associated divisible design as being isomorphic to a substructure of a finite affine space. AMS Classification: 05B05, 05B30, 20B25, 51N10

This article is a contribution to the study of the automorphism groups of 2−(v, k, 1) designs. Let D be 2−(v, 13, 1) design, G ≤ Aut(D) be block transitive, point primitive but not flag transitive. Then Soc(G), the socle of G, is not classical simple group over finite filed GF (q)(q odd). Mathematics Subject Classification: 05B05, 20B25

In this paper we consider the uniformly resolvable decompositions of the complete graph Kv , or the complete graph minus a 1-factor as appropriate, into subgraphs such that each resolution class contains only blocks isomorphic to the same graph. We completely determine the spectrum for the case in which all the resolution classes are either P3 or K3. AMS classification: 05B05.