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]
CODING theory, POLYNOMIALS, SET theory, EXISTENCE theorems, MATRICES (Mathematics), MATHEMATICAL analysis
Abstract
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]