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A correction and improvements of some recent results on walsh transforms of gold type and Kasami-Welch type functions
Date
2017-01-01
Author
Coşgun, Ayhan
Özbudak, Ferruh
Metadata
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
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We give explicit evaluations of Walsh transforms of Gold type functions f(x) = Tr-K (x(2a +1) + x(2b +1)), 0 <=< a < b when gcd (b - a, k) = gcd (b + a, k) and Kasami-Welch type functions f (x) = Tr-K (2(ta+1)/x(2a +1)), when t is odd, gcd (2(k) - 1,2(a) + 1) = 1, k is even. Therefore we correct a recent result of Roy'2012, we solve an open problem stated in Roy'2012 and we improve and generalize some results of Roy'2012 and Lahtonen-McGuire-Ward'2007.
Subject Keywords
Finite fields
,
Gold type functions
,
Kasami-Welch type functions
,
Walsh transform
URI
https://hdl.handle.net/11511/34283
DOI
https://doi.org/10.1007/978-3-319-55227-9_17
Collections
Department of Mathematics, Conference / Seminar