Bent functions embedded into the recursive framework of $${\mathbb{Z}}$$ -bent functions
Abstract Suppose that n is even. Let $${\mathbb{F}_2}$$ denote the two-element field and $${\mathbb{Z}}$$ the set of integers. Bent functions can be defined as ± 1-valued functions on $${\mathbb{F}_2^n}$$ with ± 1-valued Fourier transform. More generally we call a mapping f on $${\mathbb{F}_2^n}$$ a...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Dobbertin, Hans [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2008 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, LLC 2008 |
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| Übergeordnetes Werk: |
Enthalten in: Designs, codes and cryptography - Springer US, 1991, 49(2008), 1-3 vom: 08. Apr., Seite 3-22 |
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| Übergeordnetes Werk: |
volume:49 ; year:2008 ; number:1-3 ; day:08 ; month:04 ; pages:3-22 |
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| DOI / URN: |
10.1007/s10623-008-9189-3 |
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| 520 | |a Abstract Suppose that n is even. Let $${\mathbb{F}_2}$$ denote the two-element field and $${\mathbb{Z}}$$ the set of integers. Bent functions can be defined as ± 1-valued functions on $${\mathbb{F}_2^n}$$ with ± 1-valued Fourier transform. More generally we call a mapping f on $${\mathbb{F}_2^n}$$ a $${\mathbb{Z}}$$ -bent function if both f and its Fourier transform $${\widehat{f}}$$ are integer-valued. $${\mathbb{Z}}$$ -bent functions f are separated into different levels, depending on the size of the maximal absolute value attained by f and $${\widehat{f}}$$ . It is shown how $${\mathbb{Z}}$$ -bent functions of lower level can be built up recursively by gluing together $${\mathbb{Z}}$$ -bent functions of higher level. This recursion comes down at level zero, containing the usual bent functions. In the present paper we start to study bent functions in the framework of $${\mathbb{Z}}$$ -bent functions and give some guidelines for further research. | ||
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10.1007/s10623-008-9189-3 doi (DE-627)OLC2027288953 (DE-He213)s10623-008-9189-3-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Dobbertin, Hans verfasserin aut Bent functions embedded into the recursive framework of $${\mathbb{Z}}$$ -bent functions 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2008 Abstract Suppose that n is even. Let $${\mathbb{F}_2}$$ denote the two-element field and $${\mathbb{Z}}$$ the set of integers. Bent functions can be defined as ± 1-valued functions on $${\mathbb{F}_2^n}$$ with ± 1-valued Fourier transform. More generally we call a mapping f on $${\mathbb{F}_2^n}$$ a $${\mathbb{Z}}$$ -bent function if both f and its Fourier transform $${\widehat{f}}$$ are integer-valued. $${\mathbb{Z}}$$ -bent functions f are separated into different levels, depending on the size of the maximal absolute value attained by f and $${\widehat{f}}$$ . It is shown how $${\mathbb{Z}}$$ -bent functions of lower level can be built up recursively by gluing together $${\mathbb{Z}}$$ -bent functions of higher level. This recursion comes down at level zero, containing the usual bent functions. In the present paper we start to study bent functions in the framework of $${\mathbb{Z}}$$ -bent functions and give some guidelines for further research. Boolean function Bent function Recursive Construction Leander, Gregor aut Enthalten in Designs, codes and cryptography Springer US, 1991 49(2008), 1-3 vom: 08. Apr., Seite 3-22 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:49 year:2008 number:1-3 day:08 month:04 pages:3-22 https://doi.org/10.1007/s10623-008-9189-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_4126 AR 49 2008 1-3 08 04 3-22 |
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10.1007/s10623-008-9189-3 doi (DE-627)OLC2027288953 (DE-He213)s10623-008-9189-3-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Dobbertin, Hans verfasserin aut Bent functions embedded into the recursive framework of $${\mathbb{Z}}$$ -bent functions 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2008 Abstract Suppose that n is even. Let $${\mathbb{F}_2}$$ denote the two-element field and $${\mathbb{Z}}$$ the set of integers. Bent functions can be defined as ± 1-valued functions on $${\mathbb{F}_2^n}$$ with ± 1-valued Fourier transform. More generally we call a mapping f on $${\mathbb{F}_2^n}$$ a $${\mathbb{Z}}$$ -bent function if both f and its Fourier transform $${\widehat{f}}$$ are integer-valued. $${\mathbb{Z}}$$ -bent functions f are separated into different levels, depending on the size of the maximal absolute value attained by f and $${\widehat{f}}$$ . It is shown how $${\mathbb{Z}}$$ -bent functions of lower level can be built up recursively by gluing together $${\mathbb{Z}}$$ -bent functions of higher level. This recursion comes down at level zero, containing the usual bent functions. In the present paper we start to study bent functions in the framework of $${\mathbb{Z}}$$ -bent functions and give some guidelines for further research. Boolean function Bent function Recursive Construction Leander, Gregor aut Enthalten in Designs, codes and cryptography Springer US, 1991 49(2008), 1-3 vom: 08. Apr., Seite 3-22 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:49 year:2008 number:1-3 day:08 month:04 pages:3-22 https://doi.org/10.1007/s10623-008-9189-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_4126 AR 49 2008 1-3 08 04 3-22 |
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10.1007/s10623-008-9189-3 doi (DE-627)OLC2027288953 (DE-He213)s10623-008-9189-3-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Dobbertin, Hans verfasserin aut Bent functions embedded into the recursive framework of $${\mathbb{Z}}$$ -bent functions 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2008 Abstract Suppose that n is even. Let $${\mathbb{F}_2}$$ denote the two-element field and $${\mathbb{Z}}$$ the set of integers. Bent functions can be defined as ± 1-valued functions on $${\mathbb{F}_2^n}$$ with ± 1-valued Fourier transform. More generally we call a mapping f on $${\mathbb{F}_2^n}$$ a $${\mathbb{Z}}$$ -bent function if both f and its Fourier transform $${\widehat{f}}$$ are integer-valued. $${\mathbb{Z}}$$ -bent functions f are separated into different levels, depending on the size of the maximal absolute value attained by f and $${\widehat{f}}$$ . It is shown how $${\mathbb{Z}}$$ -bent functions of lower level can be built up recursively by gluing together $${\mathbb{Z}}$$ -bent functions of higher level. This recursion comes down at level zero, containing the usual bent functions. In the present paper we start to study bent functions in the framework of $${\mathbb{Z}}$$ -bent functions and give some guidelines for further research. Boolean function Bent function Recursive Construction Leander, Gregor aut Enthalten in Designs, codes and cryptography Springer US, 1991 49(2008), 1-3 vom: 08. Apr., Seite 3-22 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:49 year:2008 number:1-3 day:08 month:04 pages:3-22 https://doi.org/10.1007/s10623-008-9189-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_4126 AR 49 2008 1-3 08 04 3-22 |
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Abstract Suppose that n is even. Let $${\mathbb{F}_2}$$ denote the two-element field and $${\mathbb{Z}}$$ the set of integers. Bent functions can be defined as ± 1-valued functions on $${\mathbb{F}_2^n}$$ with ± 1-valued Fourier transform. More generally we call a mapping f on $${\mathbb{F}_2^n}$$ a $${\mathbb{Z}}$$ -bent function if both f and its Fourier transform $${\widehat{f}}$$ are integer-valued. $${\mathbb{Z}}$$ -bent functions f are separated into different levels, depending on the size of the maximal absolute value attained by f and $${\widehat{f}}$$ . It is shown how $${\mathbb{Z}}$$ -bent functions of lower level can be built up recursively by gluing together $${\mathbb{Z}}$$ -bent functions of higher level. This recursion comes down at level zero, containing the usual bent functions. In the present paper we start to study bent functions in the framework of $${\mathbb{Z}}$$ -bent functions and give some guidelines for further research. © Springer Science+Business Media, LLC 2008 |
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Abstract Suppose that n is even. Let $${\mathbb{F}_2}$$ denote the two-element field and $${\mathbb{Z}}$$ the set of integers. Bent functions can be defined as ± 1-valued functions on $${\mathbb{F}_2^n}$$ with ± 1-valued Fourier transform. More generally we call a mapping f on $${\mathbb{F}_2^n}$$ a $${\mathbb{Z}}$$ -bent function if both f and its Fourier transform $${\widehat{f}}$$ are integer-valued. $${\mathbb{Z}}$$ -bent functions f are separated into different levels, depending on the size of the maximal absolute value attained by f and $${\widehat{f}}$$ . It is shown how $${\mathbb{Z}}$$ -bent functions of lower level can be built up recursively by gluing together $${\mathbb{Z}}$$ -bent functions of higher level. This recursion comes down at level zero, containing the usual bent functions. In the present paper we start to study bent functions in the framework of $${\mathbb{Z}}$$ -bent functions and give some guidelines for further research. © Springer Science+Business Media, LLC 2008 |
| abstract_unstemmed |
Abstract Suppose that n is even. Let $${\mathbb{F}_2}$$ denote the two-element field and $${\mathbb{Z}}$$ the set of integers. Bent functions can be defined as ± 1-valued functions on $${\mathbb{F}_2^n}$$ with ± 1-valued Fourier transform. More generally we call a mapping f on $${\mathbb{F}_2^n}$$ a $${\mathbb{Z}}$$ -bent function if both f and its Fourier transform $${\widehat{f}}$$ are integer-valued. $${\mathbb{Z}}$$ -bent functions f are separated into different levels, depending on the size of the maximal absolute value attained by f and $${\widehat{f}}$$ . It is shown how $${\mathbb{Z}}$$ -bent functions of lower level can be built up recursively by gluing together $${\mathbb{Z}}$$ -bent functions of higher level. This recursion comes down at level zero, containing the usual bent functions. In the present paper we start to study bent functions in the framework of $${\mathbb{Z}}$$ -bent functions and give some guidelines for further research. © Springer Science+Business Media, LLC 2008 |
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Bent functions embedded into the recursive framework of $${\mathbb{Z}}$$ -bent functions |
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