Abstract:
We obtain a local limit theorem for the distribution of the vector (of growing dimension) consisting of some spectral coefficients of a random binary function of n variables as n→∞. We correct a mistake in the asymptotic formula for the number of correlation-immune functions of order k obtained in previous author's paper. We prove an asymptotic formula for the number of (n,1,k)-resilient functions as n→∞ and
k=k(n)=o(√n).
Received: 09.11.1999
Bibliographic databases:
UDC:519.7
Language: Russian
Citation:
O. V. Denisov, “A local limit theorem for the distribution of a part of the spectrum of a random binary function”, Diskr. Mat., 12:1 (2000), 82–95; Discrete Math. Appl., 10:1 (2000), 87–101
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\paper A local limit theorem for the distribution of a part of the spectrum of a random binary function
\jour Diskr. Mat.
\yr 2000
\vol 12
\issue 1
\pages 82--95
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\jour Discrete Math. Appl.
\yr 2000
\vol 10
\issue 1
\pages 87--101
Linking options:
https://www.mathnet.ru/eng/dm314
https://doi.org/10.4213/dm314
https://www.mathnet.ru/eng/dm/v12/i1/p82
This publication is cited in the following 14 articles:
K. N. Pankov, “Uluchshennye otsenki dlya chisla k-elastichnykh i korrelyatsionno-immunnykh dvoichnykh otobrazhenii”, PDM. Prilozhenie, 2021, no. 14, 48–51
Pankov K., “Enumeration of Boolean Mapping With Given Cryptographic Properties For Personal Data Protection in Blockchain Data Storage”, Proceedings of the 24Th Conference of Open Innovations Association (Fruct), Proceedings Conference of Open Innovations Association Fruct, IEEE, 2019, 300–306
K. N. Pankov, “Rekurrentnye formuly dlya chisla k-elastichnykh i korrelyatsionno-immunnykh dvoichnykh otobrazhenii”, PDM. Prilozhenie, 2019, no. 12, 62–66
Potapov V.N., “A Lower Bound on the Number of Boolean Functions With Median Correlation Immunity”, 2019 Xvi International Symposium Problems of Redundancy in Information and Control Systems (Redundancy), International Symposium Problems of Redundancy in Information and Control Systems, IEEE, 2019, 45–46
K. N. Pankov, “Improved asymptotic estimates for the numbers of correlation-immune and k-resilient vectorial Boolean functions”, Discrete Math. Appl., 29:3 (2019), 195–213
K. N. Pankov, “Uluchshennye asimptoticheskie otsenki dlya chisla korrelyatsionno-immunnykh dvoichnykh funktsii i otobrazhenii”, PDM. Prilozhenie, 2018, no. 11, 49–52
K. N. Pankov, “Utochnennye asimptoticheskie otsenki dlya chisla (n,m,k)-ustoichivykh dvoichnykh otobrazhenii”, PDM. Prilozhenie, 2017, no. 10, 46–49
Cusick T. Stanica P., “Cryptographic Boolean Functions and Applications, 2Nd Edition”, Cryptographic Boolean Functions and Applications, 2Nd Edition, Academic Press Ltd-Elsevier Science Ltd, 2017, 1–275
Etherington C.J., Anderson M.W., Bach E., Butler J.T., Stanica P., “A Parallel Approach in Computing Correlation Immunity up to Six Variables”, Int. J. Found. Comput. Sci., 27:4 (2016), 511–528
Citation in format AMSBIB
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