The Constructions Of New Families Of Hadamard Matrices

Hadamard matrix as an orthogonal matrix was initially proposed by Sylvester in 1 867.Then the Hadamard matrix was not merely applied to coding theory and cryptogra-phy,also extensively penetrated into graph theory and combination design.As one of its important components,the construction of Hadamard matrix has attracted much attention in recent years.Based on the existing construction results and the Scarpis theorem,this thesis proposes the recursive construction of new families of Hadamard matrices.The details are presented as followsSome preliminary knowledge and the existing results related to the construction of Hadamard matrix are introduced in Chapter].From the existing Hadamard matrix con-structions,we describe how to regard the Hadamard matrix as an encoding and propose the innovations of this thesisBased on the construction of an order 2(q+1)Hadamard matrix,we propose two new methods for constructing Hadamard matrices of order 2q(q+1)in Chapter 2,where the prime power q=4n+1 with n being a non-negative integerBy using the results of Latin square for constructing the Hadamard matrix of order m,we present the new constructions of Hadamard matrices of order m(m-1),order m(m/2-1)and order m(m/k-1)in Chapter 3,respectively,where k is a multiple of four that divides m into an even number.In Chapter 4,we conclude this thesis and derive some Hadamard matrix construction problems that still need to be solved.