Eigenspaces of the discrete Walsh transform |
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Authors: | M S Bespalov |
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Affiliation: | 1.Vladimir State University,Vladimir,Russia |
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Abstract: | We refine the notion of a discrete Walsh function and generalize the notion of a discrete Walsh transform, for which we propose
a method for generating a corresponding W-matrix. We propose spectral decompositions of the discrete Walsh transform operators in arbitrary enumerations, as well as
methods for finding bases of eigenspaces, one of them using a new direct product of matrices. We propose a notation for the
fast discrete Walsh transform algorithm in the Paley enumeration. We construct Parseval frames for eigenspaces of the discrete
Walsh transform in the Paley enumeration and demonstrate methods for applying them in error detection and correction. |
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Keywords: | |
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