Quasi-hadamard matrix

Ki Hyeon Park; Hong Yeop Song

doi:10.1109/ISIT.2010.5513675

Quasi-hadamard matrix

Ki Hyeon Park, Hong Yeop Song

Department of Electrical and Electronic Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings
Pages	1243-1247
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2010.5513675
Publication status	Published - 2010
Event	2010 IEEE International Symposium on Information Theory, ISIT 2010 - Austin, TX, United States Duration: 2010 Jun 13 → 2010 Jun 18

Publication series

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

Other

Other	2010 IEEE International Symposium on Information Theory, ISIT 2010
Country/Territory	United States
City	Austin, TX
Period	10/6/13 → 10/6/18

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

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10.1109/ISIT.2010.5513675

Cite this

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title = "Quasi-hadamard matrix",

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.",

author = "Park, {Ki Hyeon} and Song, {Hong Yeop}",

year = "2010",

doi = "10.1109/ISIT.2010.5513675",

language = "English",

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series = "IEEE International Symposium on Information Theory - Proceedings",

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booktitle = "2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings",

note = "2010 IEEE International Symposium on Information Theory, ISIT 2010 ; Conference date: 13-06-2010 Through 18-06-2010",

}

Park, KH & Song, HY 2010, Quasi-hadamard matrix. in 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings., 5513675, IEEE International Symposium on Information Theory - Proceedings, pp. 1243-1247, 2010 IEEE International Symposium on Information Theory, ISIT 2010, Austin, TX, United States, 10/6/13. https://doi.org/10.1109/ISIT.2010.5513675

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AU - Song, Hong Yeop

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AB - 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.

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BT - 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings

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ER -

Quasi-hadamard matrix

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