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English version: Journal of Applied and Industrial Mathematics, 2016, 10:3, 397403 

Volume 23, No 3, 2016, P. 93106 UDC 519.7
Keywords: subspace, metrically regular set, metric complement, completely regular code, bentfunction. DOI: 10.17377/daio.2016.23.513 Alexey K. Oblaukhov ^{1} Received 22 September 2015 References[1] F. J. MacWilliams and N. J. A. Sloane, The Theory of ErrorCorrecting Codes, NorthHolland, Amsterdam, 1977 (NorthHolland Math. Libr., Vol. 16). Translated under the title Teoriya kodov, ispravlyayushchikh oshibki, Svyaz’, Moscow, 1979.[2] C. Carlet, Lower bounds on the higher order nonlinearities of Boolean functions and their applications to the inverse function, in Proc. 2008 IEEE Inf. Theory Workshop, Porto, Portugal, May 5–9, 2008, pp. 333–337, IEEE, Piscataway, 2008. [3] S. Kavut, S. Maitra, and M. D. Yucel, Search for Boolean functions with excellent profiles in the rotation symmetric class, IEEE Trans. Inf. Theory, 53, No. 5, 1743–1751, 2007. [4] S. Maitra and P. Sarkar, Maximum nonlinearity of symmetric Boolean functions on odd number of variables, IEEE Trans. Inf. Theory, 48, No. 9, 2626–2630, 2002. [5] A. Neumaier, Completely regular codes, Discrete Math., 106, 353–360, 1992. [6] O. S. Rothaus, On “bent” functions, J. Comb. Theory, Ser. A, 20, No. 3, 300–305, 1976. [7] G. Sun and C. Wu, The lower bound on the secondorder nonlinearity of a class of Boolean functions with high nonlinearity, Appl. Algebra Eng. Commun. Comput., 22, No. 1, 37–45, 2011. [8] N. N. Tokareva, Duality between bent functions and affine functions, Discrete Math., 312, No. 3, 666–670, 2012. [9] N. N. Tokareva, Bent Functions: Results and Applications to Cryptography, Academic Press, San Diego, 2015. 

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