Hadamard equivalence of binary matrices

Ki Hyeon Park, Hong Yeop Song

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

3 Citations (Scopus)

Abstract

In this paper, we propose a fast algorithm for checking the Hadamard equivalence of two binary matrices, and give an intuitive analysis on its time complexity. For this, we define Hadamard-equivalence on the set of binary matrices, and a function which induces a total order on them. With respect to this order relation, we define the minimal element which is used as a representative of an equivalence class. We applied the proposed algorithm to Hadamard matrices of smaller sizes, and show the results. Especially, the result for those of Payley type I and II of the same size 60 shows they are not equivalent. Finally, we discuss a new combinatorial problem of counting the number of and enumerating all the inequivalent binary minimal matrices of size mxn, and show the solutions for small values of m, n ≤ 4, leaving many of the observed properties as open problems.

Original languageEnglish
Title of host publication2009 15th Asia-Pacific Conference on Communications, APCC 2009
Pages454-458
Number of pages5
DOIs
Publication statusPublished - 2009 Dec 1
Event2009 15th Asia-Pacific Conference on Communications, APCC 2009 - Shanghai, China
Duration: 2009 Oct 82009 Oct 10

Publication series

Name2009 15th Asia-Pacific Conference on Communications, APCC 2009

Other

Other2009 15th Asia-Pacific Conference on Communications, APCC 2009
CountryChina
CityShanghai
Period09/10/809/10/10

Fingerprint

equivalence
Hadamard matrices
Equivalence classes
Values

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Hardware and Architecture
  • Electrical and Electronic Engineering
  • Communication

Cite this

Park, K. H., & Song, H. Y. (2009). Hadamard equivalence of binary matrices. In 2009 15th Asia-Pacific Conference on Communications, APCC 2009 (pp. 454-458). [5375595] (2009 15th Asia-Pacific Conference on Communications, APCC 2009). https://doi.org/10.1109/APCC.2009.5375595
Park, Ki Hyeon ; Song, Hong Yeop. / Hadamard equivalence of binary matrices. 2009 15th Asia-Pacific Conference on Communications, APCC 2009. 2009. pp. 454-458 (2009 15th Asia-Pacific Conference on Communications, APCC 2009).
@inproceedings{a94cfaf70e8e49b2b2d8aec30ebfd54b,
title = "Hadamard equivalence of binary matrices",
abstract = "In this paper, we propose a fast algorithm for checking the Hadamard equivalence of two binary matrices, and give an intuitive analysis on its time complexity. For this, we define Hadamard-equivalence on the set of binary matrices, and a function which induces a total order on them. With respect to this order relation, we define the minimal element which is used as a representative of an equivalence class. We applied the proposed algorithm to Hadamard matrices of smaller sizes, and show the results. Especially, the result for those of Payley type I and II of the same size 60 shows they are not equivalent. Finally, we discuss a new combinatorial problem of counting the number of and enumerating all the inequivalent binary minimal matrices of size mxn, and show the solutions for small values of m, n ≤ 4, leaving many of the observed properties as open problems.",
author = "Park, {Ki Hyeon} and Song, {Hong Yeop}",
year = "2009",
month = "12",
day = "1",
doi = "10.1109/APCC.2009.5375595",
language = "English",
isbn = "9781424447855",
series = "2009 15th Asia-Pacific Conference on Communications, APCC 2009",
pages = "454--458",
booktitle = "2009 15th Asia-Pacific Conference on Communications, APCC 2009",

}

Park, KH & Song, HY 2009, Hadamard equivalence of binary matrices. in 2009 15th Asia-Pacific Conference on Communications, APCC 2009., 5375595, 2009 15th Asia-Pacific Conference on Communications, APCC 2009, pp. 454-458, 2009 15th Asia-Pacific Conference on Communications, APCC 2009, Shanghai, China, 09/10/8. https://doi.org/10.1109/APCC.2009.5375595

Hadamard equivalence of binary matrices. / Park, Ki Hyeon; Song, Hong Yeop.

2009 15th Asia-Pacific Conference on Communications, APCC 2009. 2009. p. 454-458 5375595 (2009 15th Asia-Pacific Conference on Communications, APCC 2009).

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

TY - GEN

T1 - Hadamard equivalence of binary matrices

AU - Park, Ki Hyeon

AU - Song, Hong Yeop

PY - 2009/12/1

Y1 - 2009/12/1

N2 - In this paper, we propose a fast algorithm for checking the Hadamard equivalence of two binary matrices, and give an intuitive analysis on its time complexity. For this, we define Hadamard-equivalence on the set of binary matrices, and a function which induces a total order on them. With respect to this order relation, we define the minimal element which is used as a representative of an equivalence class. We applied the proposed algorithm to Hadamard matrices of smaller sizes, and show the results. Especially, the result for those of Payley type I and II of the same size 60 shows they are not equivalent. Finally, we discuss a new combinatorial problem of counting the number of and enumerating all the inequivalent binary minimal matrices of size mxn, and show the solutions for small values of m, n ≤ 4, leaving many of the observed properties as open problems.

AB - In this paper, we propose a fast algorithm for checking the Hadamard equivalence of two binary matrices, and give an intuitive analysis on its time complexity. For this, we define Hadamard-equivalence on the set of binary matrices, and a function which induces a total order on them. With respect to this order relation, we define the minimal element which is used as a representative of an equivalence class. We applied the proposed algorithm to Hadamard matrices of smaller sizes, and show the results. Especially, the result for those of Payley type I and II of the same size 60 shows they are not equivalent. Finally, we discuss a new combinatorial problem of counting the number of and enumerating all the inequivalent binary minimal matrices of size mxn, and show the solutions for small values of m, n ≤ 4, leaving many of the observed properties as open problems.

UR - http://www.scopus.com/inward/record.url?scp=77949445889&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949445889&partnerID=8YFLogxK

U2 - 10.1109/APCC.2009.5375595

DO - 10.1109/APCC.2009.5375595

M3 - Conference contribution

AN - SCOPUS:77949445889

SN - 9781424447855

T3 - 2009 15th Asia-Pacific Conference on Communications, APCC 2009

SP - 454

EP - 458

BT - 2009 15th Asia-Pacific Conference on Communications, APCC 2009

ER -

Park KH, Song HY. Hadamard equivalence of binary matrices. In 2009 15th Asia-Pacific Conference on Communications, APCC 2009. 2009. p. 454-458. 5375595. (2009 15th Asia-Pacific Conference on Communications, APCC 2009). https://doi.org/10.1109/APCC.2009.5375595