Constructions Of Orthogonal Array With Variable Strength

Orthogonal arrays and covering arrays are one of important study objects in Combinatorial Design.They have many important applications in computer science and cryptography etc.Especially,they can solve the problem of interaction testing with fixed strength in software development and testing.But in some complex software testing,the interaction strength of many components is different.It couldn't be meet the requirements of software by using orthogonal arrays and covering arrays.Cohen et al.proposed the concept of variable strength covering array based on the requirement of component testing.Then Raaphorst introduced the concept of variable strength orthogonal array.Variable covering array plays an important role in computer software testing and cryptography.Especially,it can not only detect software system faults effectively,but also greatly reduce test numbers,cost and time in complex component interaction testing.Variable orthogonal array is a special form of variable covering array,which can improve test accuracy.Therefore,it is not only of theoretical important but also of great application value to construct variable strength orthogonal arrays.In this paper,we mainly study the construction of variable strength orthogonal arrays with strength 2 contained strength greater than 2.The paper is divided into three chapters: In Chapter1,we introduce the background of variable covering array and the results on variable covering array,and list some definitions and important conclusions used in the following later;In Chapter2,we give some constructions strength 2 contained strength greater than 2.Such as contains: difference matrix,finite field,Hadamard matrix and direct construction.In Chapter 3,we summarize the constructions and the existence of the variable strength orthogonal array and puts forward some further research questions.