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A covering array CAðN; t; k; v vÞ is an N Â k array such that every N Â t subarray contains all t-tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t-sets of component interactions. The particular case when t ¼ 2 (pairwise coverage) has been extensively studied, both to develop combinatorial constructions and to provide effective algorithmic search techniques. In this paper, a simple ''cut-and-paste'' construction is extended to covering arrays in which different columns (factors) admit different numbers of symbols (values); in the process an improved recursive construction for covering arrays with t ¼ 2 is derived.

Reversed Dickson polynomials over finite fields are obtained from Dickson polynomials D n (x, a) over finite fields by reversing the roles of the indeterminate x and the parameter a. We study reversed Dickson polynomials with emphasis on their permutational properties over finite fields. We show that reversed Dickson permutation polynomials (RDPPs) are closely related to almost perfect nonlinear (APN) functions. We find several families of nontrivial RDPPs over finite fields; some of them arise from known APN functions and others are new. Among RDPPs on F q with q < 200, with only one exception, all belong to the RDPP families established in this paper.

Abstract.In this note we extend the range of previously published tables of primitive polynomials over finite fields. For each p" < 1050 with p < 97 we provide a primitive polynomial of degree n over Fp . Moreover, each polynomial has the minimal number of nonzero coefficients among all primitives of degree n over Fp .

We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets a fixed number of times. We show that the existence of such an object implies the existence of a near-resolvable design. We provide examples and general constructions of these objects, some of which lead to new parameter families of near-resolvable designs on a non-prime-power number of points. Our constructions employ cyclotomy, partial difference sets, and Galois Rings.AMS classification: 94C30 51E20 94A62 05B10

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