| 《高维哈达玛矩阵理论与应用》：数学与现代科学技术丛书 |
| preface to the second edition preface to the first edition part ⅰ 2-dimensional cases chapter 1 walsh matrices 1.1 walsh functions and matrices 1.1.1 definitions 1.1.2 ordering 1.2 orthogonality and completeness 1.2.1 orthogonality 1.2.2 completeness 1.3 walsh transforms and fast algorithms 1.3.1 walsh-ordered walsh-hadamard transforms 1.3.2 hadamard-ordered walsh-hadamard transforms bibliography chapter 2 hadamard matrices 2.1 definitions 2.1.1 hadamard matrices 2.1.2 hadamard designs 2.1.3 williamson matrices 2.2 construction 2.2.1 general constructions 2.2.2 amicable hadamard matrices 2.2.3 skew hadamard matrices 2.2.4 symmetric hadamard matrices 2.3 existence 2.3.1 orth0gonal designs and hadamard matrices 2.3.2 existence results bibliography part ⅱ lower-dimensional cases chapter 3 3-dimensional hadamard matrices 3.1 definitions and constructions 3.1.1 definitions 3.1.2 constructions based on direct multiplications 3.1.3 constructions based on 2-dimensional hadamard matrices 3.2 3-dimensional hadamard matrices of order 4k + 2 3.3 3-dimensional hadamard matrices of order 4k 3.3.1 recursive constructions of perfect binary arrays 3.3.2 quasi-perfect binary arrays 3.3.3 3-dimensional hadamard matrices based on pba(2m, 2m) and pba(3.2m, 3.2m) 3.4 3-dimensional walsh matrices 3.4.1 generalized 2-dimensional walsh matrices 3.4.2 3-dimensional walsh matrices 3.4.3 3-dimensional pan-walsh matrices 3.4.4 analytic representations bibliography chapter 4 multi-dimensional walsh-hadamard transforms 4.1 conventional 2-dimensional walsh-hadamard transforms 4.1.1 2-dimensional walsh-hadamard transforms 4.1.2 definitions of 4-dimensional hadamard matrices 4.2 algebraic theory of higher-dimensional matrices 4.3 multi-dimensional walsh-hadamard transforms 4.3.1 transforms based on 3-dimensional hadamard matrices 4.3.2 transforms based on 4-dimensional hadamard matrices 4.3.3 transforms based on 6-dimensional hadamard matrices bibliography part ⅲ general higher-dimensional cases chapter 5 n-dimensional hadamard matrices of order 2 5.1 constructions of 2n hadamard matrices 5.1.1 equivalence between 2n hadamard matrices and h-boolean functions 5.1.2 existence of h-boolean functions 5.1.3 constructions of h-boolean functions 5.2 enumeration of 2" hadamard matrices 5.2.1 classification of 24 hadamard matrices 5.2.2 enumeration of 25 hadamard matrices 5.2.3 enumeration of general 2n hadamard matrices 5.3 applications 5.3.1 strict avalanche criterion and h-boolean functions 5.3.2 bent functions and h-boolean functions 5.3.3 reed-muller codes and h-boolean functions bibliography chapter 6 general higher-dimensional hadamard matrices 6.1 definitions, existences and constructions 6.1.1 n-dimensional hadamard matrices of order 2k 6.1.2 proper and improper n-dimensional hadamard matrices 6.1.3 generalized higher-dimensional hadamard matrices 6.2 higher-dimensional hadamard matrices based on perfect binary arrays 6.2.1 n-dimensional hadamard matrices based on pbas 6.2.2 construction and existence of higher-dimensional pbas 6.2.3 generalized perfect arrays 6.3 higher-dimensional hadamard matrices based on orthogonal designs 6.3.1 definitions of orthogonality 6.3.2 higher-dimensional orthogonal designs 6.3.3 higher-dimensional hadamard matrices from orthogonal designs bibliography part ⅳ applications to signal design and analysis chapter 7 design and analysis of sequences 7.1 sequences of cryptographic significance 7.1.1 enumerating boolean functions of cryptographic significance 7.1.2 constructing boolean functions of cryptographic significance 7.1.3 correlation immunity of boolean functions 7.1.4 entropy immunity of feedforward networks 7.2 correlation functions of geometric sequences 7.2.1 onthe correlation functions of a family of gold-geometric sequences 7.2.2 on the correlation functions of a family of generalized geometric sequences 7.2.3 on the correlation functions of p-ary d-form sequences 7.3 sequence pairs with mismatched filtering 7.3.1 binary sequences pairs with two-level autocorrelation functions (bspt) 7.3.2 difference set pairs 7.3.3 construction of bspts 7.3.4 periodic complementary binary sequence pairs 7.4 sequence unusual analysis 7.4.1 boolean neural network design 7.4.2 linear complexity and random sequences with period 2n 7.4.3 periodic ambiguity functions of eqc-based tfhc 7.4.4 auto-, cross-, and triple correlations of sequences bibliography chapter 8 design and analysis of arrays 8.1 costas arrays 8.1.1 correlations of costas arrays 8.1.2 algebraically constructed costas arrays 8.1.3 enumeration limitation of costas arrays 8.2 optical orthogonal codes 8.2.1 parameters bounds of optical orthogonal codes 8.2.2 truncated costas optical orthogonal codes bibliography concluding questions index |
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