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The Construction of Hadamard Matrix and Its Application

Author: WangWanJiang
Tutor: WangJunQing
School: Tianjin Polytechnic University
Course: Applied Mathematics
Keywords: Hadamard matrix Hadamard design Walsh functions Pseudo-random sequence Hadamard code
CLC: O151.21
Type: Master's thesis
Year: 2007
Downloads: 371
Quote: 3
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Hadamard matrix first as an orthogonal matrix Sylvester began to study in 1867 , occupies an important position in the block design , widely used in engineering and communications ; This article focuses on the relationship between the Hadamard matrix and the Walsh functions and pseudo-random sequence , and finally concluded with some theoretical significance and application value . We introduce the Hadamard Matrices and Their Several construction methods , and gives a simple construction method ; Hadamard matrix block design , coding theory and communications . Hadamard code as a non-linear combination of code to cater to the development of computer technology high-speed and reliable data storage system access request is made not only redundancy error control code , you should be able to high-speed parallel encoding and decoding needs. Gray code gives the relationship between the rows of a Hadamard matrix and discrete Walsh functions , since the Hadamard matrix having a good recursive , so configured such that a discrete Walsh function is simple and convenient . Pseudo-random sequence is widely used in radar, synchronization , data encryption , Hadamard design is a special symmetrical design , occupies an important position in the block design . In this paper, the Hadamard matrix relationship Hadamard design matrix K , given the pseudo-random sequence , Hadamard matrix , Hadamard equivalence of the design of the three .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Theory of algebraic equations,linear algebra > Linear Algebra > Matrix theory
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