Design theory
Authentication theory/coding theory
Proceedings of CRYPTO 84 on Advances in cryptology
The AETG System: An Approach to Testing Based on Combinatorial Design
IEEE Transactions on Software Engineering
Lower Bounds for Transversal Covers
Designs, Codes and Cryptography
A general construction for optimal cyclic packing designs
Journal of Combinatorial Theory Series A
Construction for optimal optical orthogonal codes
Discrete Mathematics - Papers on the occasion of the 65th birthday of Alex Rosa
Constructions for optimal (υ, 4, 1) optical orthogonal codes
IEEE Transactions on Information Theory
Cyclic Difference Packing and Covering Arrays
Designs, Codes and Cryptography
Covering arrays of strength 3 and 4 from holey difference matrices
Designs, Codes and Cryptography
Constructions of new orthogonal arrays and covering arrays of strength three
Journal of Combinatorial Theory Series A
A survey of methods for constructing covering arrays
Programming and Computing Software
Constructions of covering arrays of strength five
Designs, Codes and Cryptography
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A difference covering array with parameters k, n and q, or a DCA(k, n; q) for short, over a group (G, •) of order q is defined to be a k × n array (aij) with entries aij (0≤i≤k-1, 0≤j≤n - 1) from G such that, for any two distinct rows t and h (0≤t h≤k - 1), every element of G occurs in the difference list {dhj•dtj-1 : j = 0, 1,..., n - 1} at least once. It is clear that n ≥ q in a DCA(k, n; q). The equality holds if and only if a (q, k, 1) difference matrix exists. It is well known that a (q, k, 1) difference matrix does not exist, whenever q ≡ 2 (mod 4) and k ≥ 3. Thus, we have n ≥ q + 1 for these values of k and q. In this article, several constructive techniques for DCAs are presented, and used to solve completely the existence problem for a DCA(4, q + 1 ; q) with q ≡ 2 (mod 4). This complements the study for difference matrices in literature. The result is also useful in encoding systematic authentication codes, as well as in software testing and data compression problems.