111111.111111 preface.part i two-dimensional caseschapter 1 walsh matrices1.1 walsh functions and matrices1.1.1 definitions1.1.2 ordering1.2 orthogonality and completeness1.2.1 orthogonality1.2.2 completeness1.3 walsh transforms and fast algorithms1.3.1 walsh ordered walsh-hadamard transforms1.3.2 hadamard ordered walsh-hadamard transformsbibliographychapter 2 hadamard matrices2.1 definitions2.1.1 hadamard matrices2.1.2 hadamard designs2.1.3 williamson matrices2.2 construction2.2.1 general constructions.2.2.2 amicable hadamard matrices2.2.3 skew hadamard matrices2.2.4 symmetric hadamard matrices2.3 existence2.3.1 orthogonal designs and hadamard matrices2.3.2 existence resultsbibliographypart ii lower-dimensional caseschapter 3 three-dimensional hadamard matrices3.1 definitions and constructions3.1.1 definitions3.1.2 constructions based on direct multiplications3.1.3 constructions based on 2-dimensional hadamard matrices3.2 three-dimensional hadamard matrices of order 4k + 23.3 three-dimensional hadamard matrices of order 4k3.3.1 recursive constructions of perfect binary arrays3.3.2 quasi-perfect binary arrays3.3.3 3-dimensional hadamard matrices based on pba(2m, 2m) and pba(3.2m, 3.2m)3.4 three-dimensional walsh matrices3.4.1 generalized 2-dimensional walsh matrices3.4.2 3-dimensional walsh matrices3.4.3 3-dimensional pan-walsh matrices3.4.4 analytic representationsbibliography..chapter 4 multi-dimensional walsh-hadamard transforms4.1 conventional 2-dimensional walsh-hadamard transforms4.1.1 2-dimensional walsh-hadamard transforms4.1.2 definitions of 4-dimensional hadamard matrices4.2 algebralcal theory of higher-dimensional matrices4.3 multi-dimensional walsh-hadamard transforms4.3.1 transforms based on 3-dimensional hadamard matrices4.3.2 transforms based on 4-dimensional hadamard matrices4.3.3 transforms based on 6-dimensional hadamard matricesbibliographypart iii general higher-dimensional caseschapter 5 n-dimensional hadamard matrices of order 25.1 constructions of 2n hadamard matrices5.1.1 equivalence between 2n hadamard matrices and h-boolean functions5.1.2 existence of h-boolean functions5.1.3 constructions of h-boolean functions5.2 enumeration of 2n hadamard matrices5.2.1 classification of 24 hadamard matrices5.2.2 enumeration of 25 hadamard matrices5.2.3 enumeration of general 2n hadamard matrices5.3 applications5.3.1 strict avalanche criterion and h-boolean functions5.3.2 bent functions and h-boolean functions5.3.3 reed-muller codes and h-boolean functionsbibliographychapter 6 general higher-dimensional hadamard matrices6.1 definitions, existences and constructions6.1.1 n-dimensional hadamard matrices of order 2k6.1.2 proper and improper n-dimensional hadamard matrices6.1.3 generalized higher-dimensional hadamard matrices6.2 higher-dimensional hadamard matrices based on perfect binary arrays6.2.1 n-dimensional hadamard matrices based on pbas6.2.2 construction and existence of higher-dimensional pbas6.2.3 generalized perfect arrays6.3 higher-dimensional hadamard matrices based on orthogonal designs6.3.1 definitions of orthogonality6.3.2 higher-dimensional orthogonal designs6.3.3 higher-dimensional hadamard matrices from orthogonal designsbibliographyconcluding questionsindex...