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Sidel'nikov, Vladimir Michilovich
(1940–2008)

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Total publications: 35
Scientific articles: 35

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Professor
Doctor of physico-mathematical sciences (1981)
Speciality: 01.01.09 (Discrete mathematics and mathematical cybernetics)
Birth date: 1.03.1940
Keywords: coding theory; cryptography; finite matrix groups; decoding; packing and covering problems; spherical designs in metric spaces; spherical codes; orthogonal polynomials; quantum codes.

Subject:

Coding theory, Cryptography, Decoding, Some issues in algebra, Packing and covering problems (geometry), Theory of sequences, Theory of Orthogonal Polynomials, Spherical Codes, Designs.

I. Upper bounds on the cardinalities of codes in various metric spaces. E.g., in 1973 Sidelnikov substantially improved the Blichfeldt classical upper bound on the density of ball packings in Euclidean space. This was the first improvement since 1929. Also, Sidelnikov substantially improved the Elias–Bassalygo estimate of cardinalities of codes in Hamming spaces.

II. In 1971 new bounds were obtained for crosscorelation and autococorrelation p-ary sequences. Some of these bounds are tight. Some others are best known nowadays.

III. Decoding error correcting codes. Sidelnikov initiated research of decoding techniques for the case when the number of errors exceeds half of the code distance and proposed the first algorithm for decoding the Reed–Solomon code in this setting. He also proved some related results for Reed–Muller codes.

IV. New spherical codes and spherical design. Sidelnikov defined a new family of finite groups formed by unitary $p^m\times p^m$-matrices and proved some properties of this groups. These groups were used to construct new spherical codes and spherical designs. Special attention is paid to the case $=2$. In this case matrices are orthogonal and the orbit of any initial point on the unit sphere in the Euclidean space $\mathbb R^{2^m}$ is a spherical design of strength 7. This and earlier results allow to construct infinite sequence of the spherical designs of strengths 7, 9 and 11 on the unit sphere in the Euclidean space.

V. Ternary codes of length $(3^m-1)/2$ correcting up to 2 errors. In 1986 Sidelnikov and Gachkov constructed ternary quasiperfect codes having some amazing properties. Since then, no new examples of infinite sequences of quasiperfect codes were discovered.

VI. Cryptoanalysis of public-key cryptosystems. In 1992 Sidelnikov and Shestakov showed insecurity of one variant of McEliece public-key cryptosystem. This nontrivial result is appreciated as achievement in mathematical cryptography.

VII. New key agreement scheme. In 1993 Sidel'nikov et al. proposed a new construction of cryptographic protocol for generating private keys based on noncommutative groups.

Biography

1965–1990 I held various research positions in mathematical departments of military scientific institutes. Since 1990 and currently — Lomonosov University, Moscow: Chief of the laboratory of mathematical cryptography and professor of the same university. 1959–1964 — Lomonosov University, Moscow, student of department of Mechanics & Mathematics. 1966–1970 — Lomonosov University, Moscow, Ph.D student of post-graduate course at department for mathematics. 1964 — Master of Science Lomonosov University, Moscow, from department of Mechanics & Mathematics, USSR. 1971 — Ph.D. in coding theory Lomonosov University, Moscow, from department of Mechnics & Mathematics, Russia. 1981 — Ph.Sci. in mathematical cryptography from Institute of Cryptography, Moscow, Russia. A list of my works contains more than 65 titles. Teaching experience and current position in details. My career as a scientific researcher started 1965 after graduating from department of Mechanics & Mathematics of Lomonosov University first as a junior researcher and, since 1971, as senior researcher in a military cryptophytic institute, Moscow, Russian. I became a Ph.D student of the department for mathematics, Moscow State University in 1966. In 1970 I have finished post-graduate Ph.D degree, 1971, under supervision of Vladimir Levenshtein. I received my Doctor of Science degree in Mathematics and Cryptography, 1981, from Institute of Cryptography, Moscow, Russia. Since 1991 until now, I deliver a lecture course "Coding theory and cryptography" and supervise over a scientific seminar on Discrete Mathematics and Cryptography in Moscow University. Research interests: coding theory, cryptography, decoding, some fields of algebra, packing and covering problems (geometry), theory of sequences, theory of orthogonal polynomials, spherical codes, designs, quantum codes.

I am the academician of Russian Academy of Cryptography, winner of the State premium (1990).

   
Main publications:
  • V. M. Sidel'nikov. Spherical 7-designs in $2^n$-dimensial Euclidean space // Journal of Algebraic Combinatorics, 10 (1999), no. 3, 279–288.

http://www.mathnet.ru/eng/person17348
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https://mathscinet.ams.org/mathscinet/MRAuthorID/241251

Publications in Math-Net.Ru
2009
1. V. M. Sidel'nikov, O. Yu. Prikhodov, “On the construction of $(w,r)$ cover-free codes”, Probl. Peredachi Inf., 45:1 (2009),  36–40  mathnet  mathscinet  zmath; Problems Inform. Transmission, 45:1 (2009), 32–36  isi  scopus
2008
2. V. M. Sidel'nikov, L. S. Kazarin, “On a group algebra of a dihedral group and complexity of multiplication of second order matrices”, Tr. Diskr. Mat., 11:1 (2008),  109–118  mathnet
2007
3. L. S. Kazarin, V. M. Sidel'nikov, “An automorphism group of Suzuki $p$-group”, Tr. Diskr. Mat., 10 (2007),  87–96  mathnet
2006
4. L. S. Kazarin, V. M. Sidel'nikov, “On the automorphism group of a Suzuki $p$-algebra”, Mat. Zametki, 80:4 (2006),  526–535  mathnet  mathscinet  zmath  elib; Math. Notes, 80:4 (2006), 500–508  isi  scopus
5. V. M. Sidel'nikov, “McWilliams identity for associative schemes based on the automorphisms of finite groups”, Tr. Diskr. Mat., 9 (2006),  269–307  mathnet
2004
6. L. S. Kazarin, V. M. Sidel'nikov, “On an approach to the quantum codes design”, Tr. Diskr. Mat., 8 (2004),  128–138  mathnet
2003
7. V. M. Sidel'nikov, “Quantum code with code distance 5”, Tr. Diskr. Mat., 7 (2003),  176–190  mathnet
2002
8. V. M. Sidel'nikov, “Quantum Codes and Abelian Subgroups of the Extra-Special Group”, Probl. Peredachi Inf., 38:3 (2002),  34–44  mathnet  mathscinet  zmath; Problems Inform. Transmission, 38:3 (2002), 194–202
2000
9. V. M. Sidel'nikov, “Generalized Hadamard matrices and their applications”, Tr. Diskr. Mat., 3 (2000),  249–268  mathnet
1999
10. V. M. Sidel'nikov, “Orbital spherical 11-designs in which the initial point is a root of an invariant polynomial”, Algebra i Analiz, 11:4 (1999),  183–203  mathnet  mathscinet  zmath; St. Petersburg Math. J., 11:4 (2000), 673–686
11. V. M. Sidel'nikov, “Algorithms for Generation of a Common Key Using a Quantum Communication Channel”, Probl. Peredachi Inf., 35:1 (1999),  100–109  mathnet  mathscinet  zmath; Problems Inform. Transmission, 35:1 (1999), 85–92
1998
12. V. M. Sidel'nikov, S. P. Strunkov, “On the spectrum of orbit codes in the space of matrices”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1998, 5,  58–61  mathnet  mathscinet  zmath
1997
13. V. M. Sidel'nikov, “On One Finite Matrix Group and Codes on Euclidean Spheres”, Probl. Peredachi Inf., 33:1 (1997),  35–54  mathnet  mathscinet  zmath; Problems Inform. Transmission, 33:1 (1997), 29–44
14. V. M. Sidel'nikov, S. P. Strunkov, “On some arithmetical properties of orbit codes in a space of matrices”, Uspekhi Mat. Nauk, 52:6(318) (1997),  185–186  mathnet  mathscinet  zmath; Russian Math. Surveys, 52:6 (1997), 1328–1329  isi  scopus
15. V. M. Sidel'nikov, “Fast algorithms for constructing a set of labelings of discrete data files”, Tr. Diskr. Mat., 1 (1997),  251–264  mathnet  mathscinet  zmath
1994
16. V. M. Sidel'nikov, “Open coding based on Reed–Muller binary codes”, Diskr. Mat., 6:2 (1994),  3–20  mathnet  mathscinet  zmath; Discrete Math. Appl., 4:3 (1994), 191–207
17. V. M. Sidel'nikov, “Key Distribution System Based on Exponential Representations of Linear Group $GL_n(F_p)$”, Probl. Peredachi Inf., 30:4 (1994),  25–32  mathnet  mathscinet  zmath; Problems Inform. Transmission, 30:4 (1994), 310–316
18. V. M. Sidel'nikov, “Decoding Reed–Solomon Codes Beyond $(d-1)/2$ and Zeros of Multivariate Polynomials”, Probl. Peredachi Inf., 30:1 (1994),  51–69  mathnet  mathscinet  zmath; Problems Inform. Transmission, 30:1 (1994), 44–59
1993
19. V. M. Sidel'nikov, M. A. Cherepnev, V. V. Yashchenko, “Public key distribution systems based on noncommutative semigroups”, Dokl. Akad. Nauk, 332:5 (1993),  566–567  mathnet  mathscinet  zmath; Dokl. Math., 48:2 (1994), 384–386
20. V. M. Sidel'nikov, “Decoding the Reed–Solomon code when the number of errors is greater than half of the code distance”, Dokl. Akad. Nauk, 330:1 (1993),  20–23  mathnet  mathscinet  zmath; Dokl. Math., 47:3 (1993), 378–382
1992
21. V. M. Sidel'nikov, S. O. Shestakov, “On an encoding system constructed on the basis of generalized Reed–Solomon codes”, Diskr. Mat., 4:3 (1992),  57–63  mathnet  mathscinet  zmath; Discrete Math. Appl., 2:4 (1992), 439–444
22. A. G. D'yachkov, V. M. Sidel'nikov, “Entropy of Some Binary Sources”, Probl. Peredachi Inf., 28:4 (1992),  3–13  mathnet  mathscinet  zmath; Problems Inform. Transmission, 28:4 (1992), 297–307
23. V. M. Sidel'nikov, A. S. Pershakov, “Decoding of Reed?Muller Codes with a Large Number of Errors”, Probl. Peredachi Inf., 28:3 (1992),  80–94  mathnet  mathscinet  zmath; Problems Inform. Transmission, 28:3 (1992), 269–281
1991
24. V. M. Sidel'nikov, “Estimates for the number of appearances of elements on an interval of a recurrent sequence over a finite field”, Diskr. Mat., 3:2 (1991),  87–95  mathnet  mathscinet  zmath; Discrete Math. Appl., 2:5 (1992), 473–481
1989
25. I. B. Gashkov, V. M. Sidel'nikov, “Codes Associated with the Linear Fractional Group”, Probl. Peredachi Inf., 25:1 (1989),  3–15  mathnet  mathscinet  zmath; Problems Inform. Transmission, 25:1 (1989), 1–11
1988
26. I. B. Gashkov, V. M. Sidel'nikov, “Codes that are connected with a group of linear-fractional transformations”, Dokl. Akad. Nauk SSSR, 301:5 (1988),  1041–1044  mathnet  mathscinet  zmath; Dokl. Math., 38:1 (1989), 166–169
1987
27. V. M. Sidel'nikov, “On normal bases of a finite field”, Mat. Sb. (N.S.), 133(175):4(8) (1987),  497–507  mathnet  mathscinet  zmath; Math. USSR-Sb., 61:2 (1988), 485–494
1986
28. I. B. Gashkov, V. M. Sidel'nikov, “Linear Ternary Quasi-perfect Codes Correcting Double Errors”, Probl. Peredachi Inf., 22:4 (1986),  43–48  mathnet  mathscinet  zmath; Problems Inform. Transmission, 22:4 (1986), 284–288
1980
29. V. M. Sidel'nikov, “On Extremal Polynomials Used in Bounds of Code Volume”, Probl. Peredachi Inf., 16:3 (1980),  17–30  mathnet  mathscinet  zmath; Problems Inform. Transmission, 16:3 (1980), 174–186
1974
30. V. M. Sidel'nikov, “Upper Bounds for the Number of Points of a Binary Code with a Specified Code Distance”, Probl. Peredachi Inf., 10:2 (1974),  43–51  mathnet  mathscinet  zmath; Problems Inform. Transmission, 10:2 (1974), 124–131
31. V. M. Sidel'nikov, “New bounds for densest packing of spheres in $n$-dimensional Euclidean space”, Mat. Sb. (N.S.), 95(137):1(9) (1974),  148–158  mathnet  mathscinet  zmath; Math. USSR-Sb., 24:1 (1974), 147–157
1973
32. V. M. Sidel'nikov, “On the densest packing of balls on the surface of an $n$-dimensional Euclidean sphere and the number of binary code vectors with a given code distance”, Dokl. Akad. Nauk SSSR, 213:5 (1973),  1029–1032  mathnet  mathscinet  zmath
1971
33. V. M. Sidel'nikov, “On mutual correlation of sequences”, Dokl. Akad. Nauk SSSR, 196:3 (1971),  531–534  mathnet  mathscinet  zmath
34. V. M. Sidel'nikov, “Weight Spectrum of Binary Bose–Chaudhuri–Hoquinghem Codes”, Probl. Peredachi Inf., 7:1 (1971),  14–22  mathnet  mathscinet  zmath; Problems Inform. Transmission, 7:1 (1971), 11–17
1969
35. V. M. Sidel'nikov, “Some $k$-Valued Pseudo-random Sequences and Nearly Equidistant Codes”, Probl. Peredachi Inf., 5:1 (1969),  16–22  mathnet  mathscinet  zmath; Problems Inform. Transmission, 5:1 (1969), 12–16

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