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Abstract: In Suzuki (1998) [7] Suzuki gave a classification of association schemes with multiple Q-polynomial structures, allowing for one exceptional case which has five classes. In this paper, we rule out the existence of this case. Hence Suzukiʼs theorem mirrors exactly the well-known counterpart for association schemes with multiple P-polynomial structures, a result due to Eiichi Bannai and Etsuko Bannai in 1980. [Copyright &y& Elsevier]

Abstract: Let be positive integers. A -edge-colored graph is -e.c. or -existentially closed if for any disjoint sets of vertices with , there is a vertex not in such that all edges from this vertex to the set are colored by the -th color. In this paper, we give an explicit construction of a -e.c. graph of polynomial order. [Copyright &y& Elsevier]

Abstract: Let be the maximum possible minimum Hamming distance of a linear [] code over . Tables of best known linear codes exist for small fields. In this paper, linear codes over are constructed for k up to 6. The codes constructed are from the class of quasi-cyclic codes. The number of circulant matrices over is enumerated. In addition, the minimum distance of the extended quadratic residue code of length 44 is determined. [Copyright &y& Elsevier]

Let V be a normal affine ℝ-variety, and let S be a semi-algebraic subset of V (ℝ) which is Zariski dense in V . We study the subring BV (S) of ℝ [V] consisting of the polynomials that are bounded on S. We introduce the notion of S-compatible completions of V, and we prove the existence of such completions when dim(V ) ≤ 2 or S = V (ℝ). An S-compatible completion X of V yields a ring isomorphism φU(U) →̃ BV (S) for some (concretely specified) open subvariety U ⊃ V of X. We prove that BV (S) is a finitely generated ℝ-algebra if dim(V) ≤ 2 and S is open, and we show that this result becomes false in general when dim(V) ≥ 3. [ABSTRACT FROM AUTHOR]