A correction and improvements of some recent results on walsh transforms of gold type and Kasami-Welch type functions

Ayhan Coşgun; Ferruh Özbudak

doi:10.1007/978-3-319-55227-9_17

A correction and improvements of some recent results on walsh transforms of gold type and Kasami-Welch type functions

Ayhan Coşgun^*, Ferruh Özbudak

^*Corresponding author for this work

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

1 Citation (Scopus)

Abstract

We give explicit evaluations of Walsh transforms of Gold type functions (Formula presented) when gcd (b(− a, k)=gcd(b + a, k) and Kasami-Welch type functions (Formula presented),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.

Original language	English
Title of host publication	Arithmetic of Finite Fields : 6th International Workshop, WAIFI 2016, Revised Selected Papers
Number of pages	15
Publisher	Springer VS
Publication date	2017
Pages	243-257
ISBN (Print)	978-3-319-55226-2
ISBN (Electronic)	978-3-319-55227-9
DOIs	https://doi.org/10.1007/978-3-319-55227-9_17
Publication status	Published - 2017
Event	6th International Workshop on Arithmetic of Finite Fields, WAIFI 2016 - Ghent, Belgium Duration: 13 Jul 2016 → 15 Jul 2016

Conference

Conference	6th International Workshop on Arithmetic of Finite Fields, WAIFI 2016
Country/Territory	Belgium
City	Ghent
Period	13/07/2016 → 15/07/2016

Series	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10064 LNCS
ISSN	0302-9743

Keywords

Finite fields
Gold type functions
Kasami-Welch type functions
Walsh transform

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Coşgun, Ayhan ; Özbudak, Ferruh. / A correction and improvements of some recent results on walsh transforms of gold type and Kasami-Welch type functions. Arithmetic of Finite Fields: 6th International Workshop, WAIFI 2016, Revised Selected Papers. Springer VS, 2017. pp. 243-257 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 10064 LNCS).

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title = "A correction and improvements of some recent results on walsh transforms of gold type and Kasami-Welch type functions",

abstract = "We give explicit evaluations of Walsh transforms of Gold type functions (Formula presented) when gcd (b(− a, k)=gcd(b + a, k) and Kasami-Welch type functions (Formula presented),when t is odd, gcd (2k − 1, 2a +1) =1,k is even. Therefore we correct a recent result of Roy{\textquoteright}2012, we solve an open problem stated in Roy{\textquoteright}2012 and we improve and generalize some results of Roy{\textquoteright}2012 and Lahtonen-McGuire-Ward{\textquoteright}2007.",

keywords = "Finite fields, Gold type functions, Kasami-Welch type functions, Walsh transform",

author = "Ayhan Co{\c s}gun and Ferruh {\"O}zbudak",

year = "2017",

doi = "10.1007/978-3-319-55227-9_17",

language = "English",

isbn = "978-3-319-55226-2",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer VS",

pages = "243--257",

booktitle = "Arithmetic of Finite Fields",

note = "6th International Workshop on Arithmetic of Finite Fields, WAIFI 2016 ; Conference date: 13-07-2016 Through 15-07-2016",

}

Coşgun, A & Özbudak, F 2017, A correction and improvements of some recent results on walsh transforms of gold type and Kasami-Welch type functions. in Arithmetic of Finite Fields: 6th International Workshop, WAIFI 2016, Revised Selected Papers. Springer VS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10064 LNCS, pp. 243-257, 6th International Workshop on Arithmetic of Finite Fields, WAIFI 2016, Ghent, Belgium, 13/07/2016. https://doi.org/10.1007/978-3-319-55227-9_17

A correction and improvements of some recent results on walsh transforms of gold type and Kasami-Welch type functions. / Coşgun, Ayhan; Özbudak, Ferruh.
Arithmetic of Finite Fields: 6th International Workshop, WAIFI 2016, Revised Selected Papers. Springer VS, 2017. p. 243-257 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 10064 LNCS).

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

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AU - Coşgun, Ayhan

AU - Özbudak, Ferruh

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N2 - We give explicit evaluations of Walsh transforms of Gold type functions (Formula presented) when gcd (b(− a, k)=gcd(b + a, k) and Kasami-Welch type functions (Formula presented),when t is odd, gcd (2k − 1, 2a +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.

AB - We give explicit evaluations of Walsh transforms of Gold type functions (Formula presented) when gcd (b(− a, k)=gcd(b + a, k) and Kasami-Welch type functions (Formula presented),when t is odd, gcd (2k − 1, 2a +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.

KW - Finite fields

KW - Gold type functions

KW - Kasami-Welch type functions

KW - Walsh transform

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DO - 10.1007/978-3-319-55227-9_17

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SN - 978-3-319-55226-2

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Coşgun A, Özbudak F. A correction and improvements of some recent results on walsh transforms of gold type and Kasami-Welch type functions. In Arithmetic of Finite Fields: 6th International Workshop, WAIFI 2016, Revised Selected Papers. Springer VS. 2017. p. 243-257. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 10064 LNCS). doi: 10.1007/978-3-319-55227-9_17

A correction and improvements of some recent results on walsh transforms of gold type and Kasami-Welch type functions

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