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Diskretn. Anal. Issled. Oper., 2010, Volume 17, Number 1, Pages 34–64 (Mi da599)  

This article is cited in 24 scientific papers (total in 24 papers)

Generalizations of bent functions

N. N. Tokarevaab

a S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: Bent functions (Boolean functions with extremal nonlinear properties) are intensively studied at present since they have numerous applications in cryptography, coding theory, and other areas. New statement of problems lead to appearance of many new generalizations of bent functions which are not well known to the specialists in Boolean functions. In the paper, a systematic survey of them is given. Bibl. 63.

Keywords: Boolean function, the Walsh–Hadamard transform, nonlinearity, bent function, CDMA.

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English version:
Journal of Applied and Industrial Mathematics, 2011, 5:1, 110–129

Bibliographic databases:

UDC: 519.7
Received: 22.09.2009
Revised: 21.10.2009

Citation: N. N. Tokareva, “Generalizations of bent functions”, Diskretn. Anal. Issled. Oper., 17:1 (2010), 34–64; J. Appl. Industr. Math., 5:1 (2011), 110–129

Citation in format AMSBIB
\by N.~N.~Tokareva
\paper Generalizations of bent functions
\jour Diskretn. Anal. Issled. Oper.
\yr 2010
\vol 17
\issue 1
\pages 34--64
\jour J. Appl. Industr. Math.
\yr 2011
\vol 5
\issue 1
\pages 110--129

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    This publication is cited in the following articles:
    1. N. N. Tokareva, “Novaya kombinatornaya konstruktsiya bent-funktsii”, PDM, 2010, prilozhenie № 3, 13–14  mathnet
    2. N. N. Tokareva, “The group of automorphisms of the set of bent functions”, Discrete Math. Appl., 20:5-6 (2010), 655–664  mathnet  crossref  crossref  mathscinet  elib
    3. Tokareva N., “On the number of bent functions from iterative constructions: lower bounds and hypothesis”, Adv. Math. Commun., 5:4 (2011), 609–621  crossref  mathscinet  zmath  isi  elib  scopus
    4. Tokareva N., “Duality between bent functions and affine functions”, Discrete Math., 312:3 (2012), 666–670  crossref  mathscinet  zmath  isi  elib  scopus
    5. V. A. Shishkin, “Nekotorye svoistva $q$-ichnykh bent-funktsii”, PDM. Prilozhenie, 2014, no. 7, 33–34  mathnet
    6. Xu B., “Multidimensional Fourier Transforms and Nonlinear Functions on Finite Groups”, Linear Alg. Appl., 452 (2014), 89–105  crossref  mathscinet  zmath  isi  elib  scopus
    7. Moraga C., Stankovic M., Stankovic R.S., Stojkovic S., “the Maiorana Method To Generate Multiple-Valued Bent Functions Revisited”, 2014 IEEE 44Th International Symposium on Multiple-Valued Logic (Ismvl 2014), International Symposium on Multiple-Valued Logic, IEEE, 2014, 19–24  crossref  isi  scopus
    8. Muratovic-Ribic A., Pasalic E., “a Note on Complete Polynomials Over Finite Fields and Their Applications in Cryptography”, Finite Fields their Appl., 25 (2014), 306–315  crossref  mathscinet  zmath  isi  elib  scopus
    9. V. N. Potapov, “Svoistva $p$-ichnykh bent-funktsii, nakhodyaschikhsya na minimalnom rasstoyanii drug ot druga”, PDM. Prilozhenie, 2015, no. 8, 39–43  mathnet  crossref
    10. Hodzic S., Pasalic E., “Generalized Bent Functions - Some General Construction Methods and Related Necessary and Sufficient Conditions”, Cryptogr. Commun., 7:4 (2015), 469–483  crossref  mathscinet  zmath  isi  elib  scopus
    11. Xu B., “Bentness and Nonlinearity of Functions on Finite Groups”, Des. Codes Cryptogr., 76:3 (2015), 409–430  crossref  mathscinet  zmath  isi  elib  scopus
    12. Xu B., “Dual Bent Functions on Finite Groups and $C^*$-Algebras”, J. Pure Appl. Algebr., 220:3 (2015), 1055–1073  crossref  mathscinet  isi  scopus
    13. Singh D., Bhaintwal M., Singh B.K., “Constructions of Q-Ary Functions With Good Global Avalanche Characteristics”, Int. J. Comput. Math., 92:2 (2015), 266–276  crossref  mathscinet  zmath  isi  elib  scopus
    14. Stanica P., “on Weak and Strong 2(K)-Bent Boolean Functions”, IEEE Trans. Inf. Theory, 62:5 (2016), 2827–2835  crossref  mathscinet  zmath  isi  elib  scopus
    15. A. A. Kozhevnikov, S. V. Polikarpov, K. E. Rumyantsev, “On differential properties of a symmetric cryptoalgorithm based on pseudo-dynamic substitutions”, Matem. vopr. kriptogr., 7:2 (2016), 91–102  mathnet  crossref  mathscinet  elib
    16. M. M. Glukhov, “O priblizhenii diskretnykh funktsii lineinymi funktsiyami”, Matem. vopr. kriptogr., 7:4 (2016), 29–50  mathnet  crossref  mathscinet  elib
    17. Martinsen T., Meidl W., Mesnager S., Stanica P., “Decomposing Generalized Bent and Hyperbent Functions”, IEEE Trans. Inf. Theory, 63:12 (2017), 7804–7812  crossref  mathscinet  zmath  isi  scopus
    18. Fan Yu., Xu B., “Nonlinear Functions and Difference Sets on Group Actions”, Des. Codes Cryptogr., 85:2 (2017), 319–341  crossref  mathscinet  zmath  isi  scopus
    19. Pandey Sh.K., Dass B.K., “On Walsh Spectrum of Cryptographic Boolean Function”, Def. Sci. J., 67:5 (2017), 536–541  crossref  isi
    20. Hodzic S., Pasalic E., “Generalized Bent Functions - Sufficient Conditions and Related Constructions”, Adv. Math. Commun., 11:3 (2017), 549–566  crossref  mathscinet  zmath  isi  scopus
    21. Liu H., Feng K., Feng R., “Nonexistence of Generalized Bent Functions From to Z(2)(N) to Z(M)”, Des. Codes Cryptogr., 82:3 (2017), 647–662  crossref  mathscinet  zmath  isi  scopus
    22. Moraga C., Stankovic M., Stankovic R., Stojkovic S., “On Bent and Hyper-Bent Multiple-Valued Functions”, J. Mult.-Valued Log. Soft Comput., 29:3-4 (2017), 327–354  mathscinet  isi
    23. Fan Yu., Xu B., “Fourier Transforms and Bent Functions on Finite Groups”, Des. Codes Cryptogr., 86:9 (2018), 2091–2113  crossref  mathscinet  zmath  isi  scopus
    24. Hodzic S., Pasalic E., “Construction Methods For Generalized Bent Functions”, Discrete Appl. Math., 238 (2018), 14–23  crossref  mathscinet  zmath  isi  scopus
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