Hadamard Matrices and Their Applications
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A01=K. J. Horadam
A01=Kathy Horadam
Author_K. J. Horadam
Author_Kathy Horadam
Autocorrelation
Automorphism
Block cipher
Block code
Block matrix
Boolean function
Calculation
Category=PBV
Channel capacity
Character group
Character theory
Circulant matrix
Coding theory
Coefficient
Cohomology
Combinatorial design
Commutative property
Computation
Determinant
DFT matrix
Difference set
Dimension
Dirac delta function
Division ring
Encoder
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equivalence class
Factorization
Generator matrix
Hadamard code
Hadamard matrix
Hadamard transform
Identity matrix
Incidence matrix
Invertible matrix
Linear code
Linear equation
Linear map
Matrix representation
Orthogonal array
Orthogonal matrix
Orthogonality
P-adic number
Parseval's theorem
Permutation
Permutation group
Plotkin bound
Pseudo-Hadamard transform
Quadratic residue
Quaternion group
Representation theory
Row equivalence
S-box
Scalar multiplication
Semidirect product
Special case
Spectral method
Spectral sequence
Subgroup
Summation
Surjective function
Tensor product
Theorem
Trace (linear algebra)
Transformation matrix
Transpose
Transversal (combinatorics)
Unimodular matrix
Unit vector
Unitary matrix
Von Neumann algebra
Weil pairing
Product details
- ISBN 9780691119212
- Weight: 510g
- Dimensions: 152 x 235mm
- Publication Date: 03 Dec 2006
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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In Hadamard Matrices and Their Applications, K. J. Horadam provides the first unified account of cocyclic Hadamard matrices and their applications in signal and data processing. This original work is based on the development of an algebraic link between Hadamard matrices and the cohomology of finite groups that was discovered fifteen years ago. The book translates physical applications into terms a pure mathematician will appreciate, and theoretical structures into ones an applied mathematician, computer scientist, or communications engineer can adapt and use. The first half of the book explains the state of our knowledge of Hadamard matrices and two important generalizations: matrices with group entries and multidimensional Hadamard arrays. It focuses on their applications in engineering and computer science, as signal transforms, spreading sequences, error-correcting codes, and cryptographic primitives. The book's second half presents the new results in cocyclic Hadamard matrices and their applications. Full expression of this theory has been realized only recently, in the Five-fold Constellation.
This identifies cocyclic generalized Hadamard matrices with particular "stars" in four other areas of mathematics and engineering: group cohomology, incidence structures, combinatorics, and signal correlation. Pointing the way to possible new developments in a field ripe for further research, this book formulates and discusses ninety open questions.
K. J. Horadam is Professor of Mathematics and leads the Information Theory and Security Research Group at RMIT University, Melbourne, Australia.
