Theory and Applications of Higher-Dimensional Hadamard Matrices（影印版）

　　This is the first book on higher-dimensional hadamard matrices and their application in telecommunictions and information security .It is divided into three parts according to the dimensional walsh and Hadamard matrices .Fast algorithms，updated constructions，existence results，and their generalised forms are presented. The second part deals with the lower-dimenstional cases，e.g.3-，4-，and 6- dimensional Walsh and Hadamard matrices and transforms.One of the aims of this part is to simplify moving smoothly from 2-dimensional cases to the general higher-dimensional cases.This part concentrates on the 3-dimensional Hadamard and Walsh matrices.Constructions based upon direct multiplication，and upon recursive methods，perfect binary arrays are also introduced.Another important topic is the existence and construction of 3-dimensional Hadamard matrices of orders 4k and 4k +2 respectively，and a group of transforms based on 2-，3-，4-and 6-dimensional walsh-Hadamard matrices and their corresponding fast algorithms.The third part is the key part，which investigates the N-dimensional Hadamard matrices of order 2，which have been proved equivalent to the well known H-Boolean functions and the perfect binary arrays of order 2.This equivalence motivates a group of perfect results about the enumeration of higher-dimensional Hadamard matrices of order 2. Applications of these matrices to feed forward networking ，stream cipher，Bent functions and error correction cods are presented in turn.after introducing the definitions of the regular，proper，improper，and generalised higher-dimensional Hadamard matrices ，many theorems about the existence and constructions are presented.Perfect binary arrays，generalised perfect arrays，and the orthogonal desgns are also used to construct new higher-dimensional Hadamard matrices.The many open problems in the study of the theory of higher-dimensional Hadamard matrices which are also listed in the book will encourage further research.Audience This volume will appeal to researchers and graduate students whose work involves signal processing，coding，information security and applied discrete mathematics.

暂缺《Theory and Applications of Higher-Dimensional Hadamard Matrices（影印版）》作者简介

Preface
PartITwo-DimensionalCases
Chapter1WalshMatrices
1.1WalshFunctionsandMatrices
1.1.1Definitions
1.1.2Ordering
1.2OrthogonalityandCompleteness
1.2.1Orthogonality
1.2.2Completeness
1.3WalshTransformsandFastAlgorithms
1.3.1WalshOrderedWalsh-HadamardTransforms
1.3.2HadamardOrderedWalsh-HadamardTransforms
Bibliography
Chapter2HadamardMatrices
2.1Definitions
2.1.1HadamardMatrices
2.1.2HadamardDesigns
2.1.3WilliamsonMatrices
2.2Construction
2.2.1GeneralConstructions
2.2.2AmicableHadamardMatrices
2.2.3SkewHadamardMatrices
2.2.4SymmetricHadamardMatrices
2.3Existence
2.3.1OrthogonalDesignsandHadamardMatrices
2.3.2ExistenceResults
Bibliography
PartIILower-DimensionalCases
Chapter3Three-DimensionalHadamardMatrices
3.1DefinitionsandConstructions
3.1.1Definitions
3.1.2ConstructionsBasedonDirectMultiplications
3.1.3ConstructionsBasedon2-DimensionalHadamard
Matrices
3.2Three-DimensionalHadamardMatricesofOrder4k+2
3.3Three-DimensionalHadamardMatricesofOrder4k
3.3.1RecursiveConstructionsofPerfectBinaryArrays
3.3.2Quasi-PerfectBinaryArrays
3.3.33-DimensionalHadamardMatricesBasedonPBA(2m,2m)andPBA(3.2m,3.2m)
3.4Three-DimensionalWalshMatrices
3.4.1Generalized2-DimensionalWalshMatrices
3.4.23-DimensionalWalshMatrices
3.4.33-DimensionalPan-WalshMatrices
3.4.4AnalyticRepresentations
Bibliography
Chapter4Multi-DimensionalWalsh-HadamardTransforms
4.1Conventional2-DimensionalWalsh-HadamardTransforms
4.1.12-DimensionalWalsh-HadamardTransforms
4.1.2Definitionsof4-DimensionalHadamardMatrices
4.2AlgebraicalTheoryofHigher-DimensionalMatrices
4.3Multi-DimensionalWalsh-HadamardTransforms
4.3.1TransformsBasedon3-DimensionalHadamardMatrices
4.3.2TransformsBasedon4-DimensionalHadamardMatrices
4.3.3TransformsBasedon6-DimensionalHadamardMatrices
Bibliography
PartIIIGeneralHigher-DimensionalCases
Chapter5n-DimensionalHadamardMatricesofOrder2
5.1Constructionsof2nHadamardMatrices
5.1.1EquivalenceBetween2nHadamardMatricesand
H-BooleanFunctions
5.1.2ExistenceofH-BooleanFunctions
5.1.3ConstructionsofH-BooleanFunctions
5.2Enumerationof2nHadamardMatrices
5.2.1Classificationof24HadamardMatrices
5.2.2Enumerationof25HadamardMatrices
5.2.3EnumerationofGeneral2nHadamardMatrices
5.3Applications
5.3.1StrictAvalancheCriterionandH-BooleanFunctions
5.3.2BentFunctionsandH-BooleanFunctions
5.3.3Reed-MullerCodesandH-BooleanFunctions
Bibliography
Chapter6GeneralHigher-DimensionalHadamardMatrices
6.1Definitions,ExistencesandConstructions
6.1.1n-DimensionalHadamardMatricesofOrder2k
6.1.2ProperandImpropern-DimensionalHadamardMatrices
6.1.3GeneralizedHigher-DimensionalHadamardMatrices
6.2Higher-DimensionalHadamardMatricesBasedonPerfectBinaryArrays
6.2.1n-DimensionalHadamardMatricesBasedonPBAs
6.2.2ConstructionandExistenceofHigher-DimensionalPBAs
6.2.3GeneralizedPerfectArrays
6.3Higher-DimensionalHadamardMatricesBasedonOrthogonalDesigns
6.3.1DefinitionsofOrthogonality
6.3.2Higher-DimensionalOrthogonalDesigns
6.3.3Higher-DimensionalHadamardMatricesfrom
OrthogonalDesigns
Bibliography
concludingQuestions
Index