Quasi-hadamard matrix

Ki Hyeon Park, Hong Yeop Song

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We apply the Hadamard equivalence to all the binary matrices of size m × 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 the number of HR-minimals of size m × n for m ≤ 3. Some properties and constructions of HR-minimals are investigated. HR-minimals with the largest weight on its second row are defined as Quasi-Hadamard matrices, which are very similar to Hadamard matrices in terms of the absolute correlations of pairs of rows, in the sense that they give a set of row vectors with "best possible orthogonality." We report lots of exhaustive search results and open problems, one of which is equivalent to the Hadamard conjecture.

Original languageEnglish
Title of host publication2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings
Pages1243-1247
Number of pages5
DOIs
Publication statusPublished - 2010
Event2010 IEEE International Symposium on Information Theory, ISIT 2010 - Austin, TX, United States
Duration: 2010 Jun 132010 Jun 18

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8103

Other

Other2010 IEEE International Symposium on Information Theory, ISIT 2010
CountryUnited States
CityAustin, TX
Period10/6/1310/6/18

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modelling and Simulation
  • Applied Mathematics

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