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

All Science Journal Classification (ASJC) codes

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

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  • 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