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2-perfect algorithm Anne Penfold Anne Penfold Street Applications Audit Expert Australia block design Bulletin closed trail codes codewords column Combinatorics complete graph Computer Science conference conjecture contains corresponding critical sets cycle cyclic decompositions denote Department of Mathematics differences digraphs disjoint dominating sets edges elements email address equationally defined Euler Medal example Figure Finite Fields follows geometry girth given graph G Graph Theory Hadamard Hadamard Matrices Hence Institute of Combinatorics integer isomorphic Jennifer Seberry label latin square Lemma Math Medal modulo node non-singleton component obtained optimal sequence orbit Orthogonal pair paper parallel class partition permutation points polygonal graphs polynomial problem Proof quadratic residues quasigroup queens query basis matrix R.G. Stanton regular graphs result rows secret sharing secret sharing scheme Standard Construction statistical database Steiner triple systems subgeometry subgraphs subset Suppose symmetric t-set Theorem transitive digraph trees unique University vector vertices