The Hamming Distances Of Saturated Asymmetrical Orthogonal Arrays With Strength 2

Orthogonal arrays have many connections to other combinatorial designs and are applied in coding theory,the statistical design of experiments,cryptography,various types of software testing and quality control.In this paper,we present some general methods to find the Hamming distances for saturated asymmetrical orthogonal arrays(SAOAs)with strength 2.We also provide the Hamming distances of the SAOAs constructed from difference schemes or by the expansive replacement method.As applications of our methods,the Hamming distances of SAOA parents of size less than or equal to 100 are obtained.The feasibility of Hamming distances is discussed.The thesis consists of four chapters and is organized as follows.Chapter 1 introduces the research background of the thesis,the related concepts and some existing results.In Chapter 2,On the basis of [1],we sum up some effective approachs for computing the Hamming distance of SAOAs with strength 2.We also provide the Hamming distances of the SAOAs constructed from difference schemes or by the expansive replacement method.As applications of our methods,the Hamming distances of SAOA parents of size less than or equal to 100 are obtained.Chapter 3 discusses the realization of Hamming distances.The summary of this paper is proposed in Chapter 4,we put forward some suggestions and the direction of efforts.