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A covering array t-CAðn; k; gÞ is a k Â n array on a set of g symbols with the property that in each t Â n subarray, every t Â 1 column appears at least once. This paper improves many of the best known upper bounds on n for covering arrays, 2-CAðn; k; gÞ with g þ 1 k 2g, for g ¼ 3 Á Á Á 12 by a construction which in many of these cases produces a 2-CAðn; k;… (More)
Using a generalisation of Hamiltonian cycles to uniform hypergraphs due to Katona and Kierstead, we define a new notion of a Hamiltonian decomposition of a uniform hypergraph. We then consider the problem of constructing such decompositions for complete uniform hypergraphs, and describe its relationship with other topics, such as design theory.
We consider polynomials over the binary field, F 2. A polynomial f of degree m is called primitive if k = 2 m − 1 is the smallest positive integer such that f divides x k + 1. We consider polynomials over the binary field, F 2. A polynomial f of degree m is called primitive if k = 2 m − 1 is the smallest positive integer such that f divides x k + 1.
We consider Class-Uniformly Resolvable Group Divisible Designs (CURGDD), which are resolvable group divisible designs in which each of the resolution classes has the same number of blocks of each size. We derive the fully general necessary conditions including a number of extremal bounds. We present some general constructions including a novel construction… (More)
Consider a maximum-length shift-register sequence generated by a primitive polynomial f over a finite field. The set of its subintervals is a linear code whose dual code is formed by all polynomials divisible by f. Since the minimum weight of dual codes is directly related to the strength of the corresponding orthogonal arrays, we can produce orthogonal… (More)
Complex and natural social interaction between artificial agents (computer-generated or robotic) and humans necessitates the display of rich emotions in order to be believable, socially relevant, and accepted, and to generate the natural emotional responses that humans show in the context of social interaction, such as engagement or empathy. Whereas some… (More)