Constructions Of Column-Orthogonal Strong Orthogonal Arrays

The orthogonal array is an important structure in statistics,coding theory and combinatorial design.Strong orthogonal arrays(SOAs)have better space-filling properties than ordinary orthogonal arrays for computer experiments.Strong orthogonal arrays of strength two plus,two star,three minus and three can improve the spacefilling properties in low dimensions and column orthogonality plays a vital role in computer experiments.In this thesis,we use difference matrices and generator matrices of linear codes to present several constructions of column-orthogonal strong orthogonal arrays(OSOAs)of strength two plus,two star,three minus and three.Compared with the known results,our constructions can provide more factors.Based on SOAs of stength two plus via the Addelman-Kempthorne method.we also propose a novel construction for OSOAs of strength two plus.This thesis is organized as follows.In Chapter 1,we describe backgrounds and our main results.In Chapter 2,we describe characterization of SOAs.and list construction methods of OSOAs of strength two plus,two star.three minus and three.In Chapter 3,based on the construction method of OSOAs.we use difference matrices to construct pairs of orthogonal arrays with special properties,so as to present several constructions of OSOAs of strength two plus and two star.Our OSOAs can provide more factors.In Chapter 4,we use generator matrices of linear codes to construct pairs of orthogonal arrays with special properties.so as to present several constructions of OSOAs of strength two plus,two star,three minus and three.Our OSOAs can also provide more factors.In Chapter 5,based on the construction for SOAs of strength two plus by AddelmanKempthorne method,we propose a construction for OSOAs of strength two plus.In Chapter 6,we summinarie this thesis and poses some problems for future work.