Hadamard equivalence of binary matrices
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...
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Published in | 2009 15th Asia-Pacific Conference on Communications pp. 454 - 458 |
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Main Authors | , |
Format | Conference Proceeding |
Language | English |
Published |
IEEE
01.10.2009
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Subjects | |
Online Access | Get full text |
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Summary: | 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 m×n, and show the solutions for small values of m, n ¿ 4, leaving many of the observed properties as open problems. |
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ISBN: | 9781424447848 1424447844 |
ISSN: | 2163-0771 |
DOI: | 10.1109/APCC.2009.5375595 |