New enumeration of Walsh matrices

New enumeration of Walsh matrices The discrete Walsh transform is a linear transform defined by a Walsh matrix. Three ways to construct Walsh matrices are known, which differ by the sequence order of rows and correspond to the Paley, Walsh, and Hadamard enumerations. We propose a new enumeration of Walsh matrices and study its properties. The new enumeration is constructed as a linear rearrangement; we obtain an eigenvector basis for it and propose a convenient-to-generate fast implementation algorithm; the new enumeration possesses certain symmetry properties, which make it similar to the discrete Fourier transform. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

New enumeration of Walsh matrices

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2009 by Pleiades Publishing, Ltd.
Subject
Engineering; Systems Theory, Control; Information Storage and Retrieval; Electrical Engineering; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946009040048
Publisher site
See Article on Publisher Site

Abstract

The discrete Walsh transform is a linear transform defined by a Walsh matrix. Three ways to construct Walsh matrices are known, which differ by the sequence order of rows and correspond to the Paley, Walsh, and Hadamard enumerations. We propose a new enumeration of Walsh matrices and study its properties. The new enumeration is constructed as a linear rearrangement; we obtain an eigenvector basis for it and propose a convenient-to-generate fast implementation algorithm; the new enumeration possesses certain symmetry properties, which make it similar to the discrete Fourier transform.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jan 21, 2010

References

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