Some properties of binary matrices and quasi-orthogonal signals based on hadamard equivalence

Ki Hyeon Park, Hong Yeop Song

Research output: Contribution to journalArticle

Abstract

We apply the Hadamard equivalence to all the binary ma-trices of the size m x n and study various properties of this equivalence relation and its classes. We propose to use HR-minimal as a representative of each equivalence class, and count and/or estimate the number of HR-minimals of size mxn. Some properties and constructions of HR-minimals are investigated. Especially, we figure that the weight on an HR-minimal's second row plays an important role, and introduce the concept of Quasi-Hadamard matrices (QH matrices). We show that the row vectors of mxn QH matrices form a set of m binary vectors of length n whose maximum pairwise absolute correlation is minimized over all such sets. Some prop-erties, existence, and constructions of Quasi-orthogonal sequences are also discussed. We also give a relation of these with cyclic difference sets. We report lots of exhaustive search results and open problems, one of which is equivalent to the Hadamard conjecture.

Original languageEnglish
Pages (from-to)1862-1872
Number of pages11
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE95-A
Issue number11
DOIs
Publication statusPublished - 2012 Nov

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Hadamard matrices
Equivalence
Binary
Equivalence classes
Hadamard Matrix
Row vector
Difference Set
Exhaustive Search
Equivalence relation
Equivalence class
Pairwise
Open Problems
Figure
Count
Estimate

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

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