Hadamard Matrices and Their Applications

Abstract

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Context-based texture analysis for secure revocable iris-biometric key generation

“…Hadamard codes, which are generated using Hadamard matrices, are of the type 2 n , n + 1, 2 n+1 , which means bitstreams of length n + 1 are mapped to codewords of length 2 n and the whole code consists of a total number of 2 n+1 codewords. Further details about Hadamard codes can be found in [2]. A randomly chosen codeword of a Hardamard code is XORed with the cryptographic key where both bitstreams are of the same length.…”

A Video Transmission System for Severely Degraded Channels

“…Let γ (i) be the order statistics [81] of γ i . In other words, (γ (0) , γ (1) , ..., γ (N −1) ) is a permutation of…”

“…where the code matrix, C, is an N × N block-diagonal matrix, and all diagonal components of C are equal to the L × L Hadamard matrix [1], H L , defined by…”

“…For reliable transmission, we specify that the probability of no LBC errors in B LBC blocks must be greater than 1 − ε f ail . In order to minimize distortion, we must find the optimal block parity vector t = [t 1 given the constraints…”

Expanding generalized Hadamard matrices over Gm by substituting several generalized Hadamard matrices over G

“…In this case, the notion of orthogonality should be suitably modified as in the following definition [4], [9]- [13]. We will restrict our discussion to abelian groups written additively in this paper.…”