The Construction Of Hadamard Matrix And Its Application

Hadamard matrix as an orthogonal matrix was investigated by Sylvester from 1867, possess important position in block design, it was used extensive in project and communication. The thesis has discussed the relation of Hadamard matrix and Walsh function as well as pseudo-random sequence. Finally, the conclusion we have given has certain theoretical meaning and applied value.This thesis has introduced Hadamard matrix's some kinds of construction methods and its nature, and give a simple construction. And we have given Hadamard matrix in detail in block design, coding and the specific application in communication., Hadamard code as a nonlinear combinatorial code has catered to the need of development of computer technology, stock systematic data and high speed for realizing and reliable access, request the error control code has not only little redundancy, but also can parallel encoding and decoding with high speed.Using the Gray code, we obtain the relationship between the row of Hadamard matrix and discrete Walsh function. Because Hadamard matrix has good recursion, makes the construction of discrete Walsh function is simple and convenient.Pseudo-random sequence extensive application in radar, synchronous phenomenon, encryption, Hadamard design is a kind of special symmetrical design, possess important position in block design. In this thesis, we have given pseudo-random sequence, Hadamard matrix and the equivalence of Hadamard design based on the relationship of Hadamard design and Hadamard matrix and matrix K.