ON A DESIGN FROM PRIMITIVE REPRESENTATIONS OF THE FINITE SIMPLE GROUPS

In this paper we present a design construction from primitive permutation representations of a finite simple group G. The group G acts primitively onthe points and transitively on the blocks of the design. The construction has this property that with some conditions we can obtain t-design for t >=2. We examine our design for fourteen sporadic simple groups. As a result we found a 2-(176,5,4) design with full automorphism group M22

Symmetric 1-designs from PGL2(q), for q an odd prime power

All non-trivial point and block-primitive 1-(v, k, k) designs that admit the group G = PGL2(q), where q is a power of an odd prime, as a permutation group of automorphisms are determined. These self-dual and symmetric 1-designs are constructed by defining { |M|/|M ∩ Mg|: g ∈ G } to be the set of orbit lengths of the primitive action of G on the conjugates of M

On Perfect Difference Families and their Applications to Radar Arrays

科学研究費助成事業(科学研究費補助金)研究成果報告書：基盤研究(C)2009-2011課題番号：2154010

Binary doubly-even self-dual codes of length 72 with large automorphism groups

We study binary linear codes constructed from fifty-four Hadamard 2-(71,35,17) designs. The constructed codes are self-dual, doubly-even and self-complementary. Since most of these codes have large automorphism groups, they are suitable for permutation decoding. Therefore we study PD-sets of the obtained codes. We also discuss error-correcting capability of the obtained codes by majority logic decoding. Further, we describe a construction of a strongly regular graph with parameters (126,25,8,4) from a binary [35,8,4] code related to a derived 2-(35,17,16) design