## Coding theory, design theory, group theory: proceedings of the Marshall Hall ConferenceContains papers prepared for the 1990 multidisciplinary conference held to honor the late mathematician and researcher. Topics include applications of classic geometry to finite geometries and designs; multiple transitive permutation groups; low dimensional groups and their geometry; difference sets in 2-groups; construction of Galois groups; construction of strongly p-imbeded subgroups in finite simple groups; Hall triple systems, Fisher spaces and 3-transposition groups; explicit embeddings in finitely generated groups; 2-transitive and flag transitive designs; efficient representations of perm groups; codes and combinatorial designs; optimal normal bases for finite fields; vector space designs from quadratic forms and inequalities; primitive permutation groups, graphs and relation algebras; large sets of ordered designs, orthogonal 1-factorizations and hyperovals; algebraic integers all of whose algebraic conjugates have the same absolute value. |

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### Contents

2Transitive and FlagTransitive Designs | 13 |

Codes and Combinatorial Designs | 31 |

Finite Vertex Transitive Graphs and Primitive | 51 |

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### Common terms and phrases

2-transitive abelian affine geometry affine plane affine spaces Algebra associated automorphism group Babai blocks meeting Cayley graph classification collineation groups Combinatorial complete set conjecture conjugate construction contains Corollary corresponding defined denote difference set dimension distance transitive graphs divisor elements equation exactly exists finite group flag-transitive follows frequency squares GF(q GF(qn Goppa code group G group of Lie Hadamard matrix Hence hypercubes hypergraph hyperplanes integer isomorphic Jungnickel latin squares lattice Lemma Let G Lie type linear MARSHALL HALL Mathematics matrix MEMORY OF MARSHALL normal basis normal subgroup number of edge one-factorizations overlarge set pair parallel class partition system permutation groups plane of order polynomial poset prime primitive problem projection graphs projective plane proof Proposition proved representation result s-arc set of disjoint spaces of order Steiner triple systems subset subspaces Theorem translation planes two-graph unique v-set vertex set vertex-transitive graphs vertices