Group construction of covering arrays

Abstract

There has been a lot of research on covering arrays in the last two decades and most of it includes construction, application and generalization of covering arrays. The main focus of this thesis is the group construction of covering arrays. The project was aimed at improving bounds on covering array number and thus to improve applications of covering arrays to testing systems and networks. For this purpose, we use group construction of covering arrays which has been proven to be one of the best possible method for the construction of covering arrays. A covering array CA(n; k; g), is an k£n array with entries from Zg and the property that in any pair of rows, each of the g2 ordered pairs from Zg £ Zg appear in at least one column. This property is called qualitative independence. Here, the size of the covering array is represented by parameter n and Zg represents its alphabet. A covering array is optimal if it has the minimum number of columns among covering arrays with the same number of rows. We use group construction of covering arrays with some modifications which yields new upper bounds on the size of the optimal covering arrays.