R. G. Stanton

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An Hadamard matrix H is an n by n matrix all of whose entries are +1 or — 1 which satisfies HH T = n J, H T being the transpose of H. The order n is necessarily 1, 2 or 42, with t a positive integer. R. E. A. C. Paley [3] gave construction methods for various infinite classes of Hadamard matrices, chiefly using properties of quadratic residues in finite(More)
A bstract The classical bicovering problem seeks to cover all pairs from a v-set by a family F of k-sets so that every pair occurs at least twice and the cardinality of F is minimaL A weight function is introduced for blocks in such a design, and its use in constructing bicoverings is illustrated. A covering is a collection of k-sets (blocks) chosen from(More)
A graph is singular if the zero eigenvalue is in the spectrum of its 0-1 adjacency matrix A. If an eigenvector belonging to the zero eigenspace of A has no zero entries, then the singular graph is said to be a core graph. A (κ, τ)-regular set is a subset of the vertices inducing a κ-regular subgraph such that every vertex not in the subset has τ neighbours(More)
A Costas latin square of order n is a set of n disjoint Costas arrays of the same order. Costas latin squares are studied here from a construction as well as a classification point of view. A complete classification is carried out up to order 27. In this range, we verify the conjecture that there is no Costas latin square for any odd order n ≥ 3. Various(More)
In earlier papers, we have illustrated how the packings of pairs into k-sets depend critically upon whether the total number of varieties v does or does not exceed the value k 2-k + 1. The behaviour is also critically affected by the existence or non-existence of a projective geometry on k 2-k + 1 points. From these points of view, the packings of v(More)
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