Vladimir Levenshtein

Levenshtein graduated from Moscow State University in 1958, where he studied in the faculty of Mechanics and Mathematics. He was a member of the student Komsomol organization and was in charge of university preparations for the 6th World Festival of Youth and Students.^[3]

After graduation, he worked at the M.V Keldysh Institute of Applied Mathematics.

• Levenshtein, V. I. (1965), "Binary codes capable of correcting deletions, insertions, and reversals.", Doklady Akademii Nauk SSSR, 163 (4): 845–848
• Delsarte, P.; Levenshtein, V. I. (1998), "Association schemes and coding theory", IEEE Transactions on Information Theory, 44 (6): 2477–2504, Bibcode:1998ITIT...44.2477D, doi:10.1109/18.720545
• V.I. Levenshtein (1960), "On a class of systematic codes", Doklady Akademii Nauk SSSR, 131 (5): 1011–1014
• V.I. Levenshtein, Application of Hadamard matrices to a problem in coding theory, Problems of Cybernetics, vol. 5, GIFML, Moscow, 1961, 125–136.
• V.I. Levenshtein (1961), "Certain properties of code systems", Doklady Akademii Nauk SSSR, 140 (6): 1274–1277
• V.I. Levenshtein (1961), "Self-adaptive automata for decoding messages", Doklady Akademii Nauk SSSR, 141 (6): 1320–1323
• V.I. Levenshtein (1962), "On the inversion of finite automata", Doklady Akademii Nauk SSSR, 147 (6): 1300–1303
• V.I. Levenshtein, On the stable extension of finite automata, Problems of Cybernetics, vol. 10, GIFML, Moscow, 1963, 281–286.
• V.I. Levenshtein, On some coding systems and self-tuning machines for decoding messages, Problems of Cybernetics, vol. 11, GIFML, Moscow, 1964, 63–121.
• V.I. Levenshtein, Decoding automata invariant with respect to the initial state, Problems of Cybernetics, vol. 12, GIFML, Moscow, 1964, 125–136.
• V.I. Levenshtein (1965), "Binary codes with correction for deletions and insertions of the symbol 1", Problemy Peredachi Informatsii, 1 (1): 12–25
• V.I. Levenshtein (1965), "On a Method of Solving the Problem of Synchronizing a Chain of Automata in Minimal Time", Problemy Peredachi Informatsii, 1 (4): 20–32
• V.I. Levenshtein, Binary codes providing synchronization and correction of errors, Abstracts of short scientific reports of the International Congress of Mathematicians, Section 13, Moscow, 1966, 24.
• V.I. Levenshtein, Asymptotically optimal binary code with correction of occurrences of one or two adjacent characters, Problems of Cybernetics, vol. 19, Science, Moscow, 1967, 293–298.
• V.I. Levenshtein, On the redundancy and deceleration of separable coding of natural numbers, Problems of Cybernetics, vol. 20, Nauka, Moscow, 1968, 173–179.
• V.I. Levenshtein (1968), "On the Synchronization of Two-Way Networks of Automata", Problemy Peredachi Informatsii, 4 (4): 49–62
• V.I. Levenshtein (1969), "Bounds for Codes Ensuring Error Correction and Synchronization", Problemy Peredachi Informatsii, 5 (2): 3–13
• V.I. Levenshtein (1970), "On the Maximum Number of Words in Codes without Overlapping", Problemy Peredachi Informatsii, 6 (4): 88–90
• V.I. Levenshtein (1971), "One Method of Constructing Quasilinear Codes Providing Synchronization in the Presence of Errors", Problemy Peredachi Informatsii, 7 (3): 30–40
• V.I. Levenshtein (1971), "Upper-Bound Estimates for Fixed-Weight Codes", Problemy Peredachi Informatsii, 7 (4): 3–12
• V.I. Levenshtein (1974), "Minimum Redundancy of Binary Error-Correcting Codes", Problemy Peredachi Informatsii, 10 (2): 26–42
• V.I. Levenshtein, Elements of coding theory, In the book. Discrete mathematics and mathematical questions of cybernetics, Nauka, Moscow, 1974, 207–305.
• V.I. Levenshtein (1975), "Maximal packing density of n-dimensional Euclidean space with equal balls", Matematicheskie Zametki, 18 (2): 301–311.
• VI Levenshtein, Methods for obtaining bounds in metric problems of coding theory, Proc. of the 1975 IEEE-USSR Joint Workshop on Information Theory, New York, 1976, 126–143.
• V.I. Levenshtein (1977), "Bounds on the Probability of Undetected Error", Problemy Peredachi Informacii, 13 (1): 3–18
• G.A. Kabatiansky; V.I. Levenshtein (1978), "On Bounds for Packings on a Sphere and in Space", Problemy Peredachi Informatsii, 14 (1): 3–25
• V.I. Levenshtein, On the choice of polynomials for obtaining boundaries in packaging problems, VII All-Union Conference on the Theory of Coding and Information Transfer, Part II, Moscow - Vilnius, 1978, 103–108.
• V.I. Levenshtein (1979), "On boundaries for packings in n-dimensional Euclidean space", Doklady Akademii Nauk SSSR, 245 (6): 1299–1303
• V.I. Levenshtein (1982), "Bounds of the maximal capacity of a code with a limited scalar product modulus", Doklady Akademii Nauk SSSR, 263 (6): 1303–1308
• V.I. Levenshtein, Borders for packaging of metric spaces and some of their applications, Problems of cybernetics, vol. 40, Science, Moscow, 1983, 43–110.
• VI Levenshtein, Packing of polynomial metric spaces, Third International Workshop on Information Theory, Convolutional codes; multi-user communication, Sochi, 1987, 271–274.
• V.I. Levenshtein (1989), "On the Straight-Line Bound for the Undetected Error Exponent", Problemy Peredachi Informatsii, 25 (1): 33–37
• VI Levenshtein, Perfect deletion-correcting codes as combinatorial designs, Proc. of the Second International Workshop: Algebraic and Combinatorial Coding Theory, Leningrad, USSR, 1990, 137–140.
• V.I. Levenshtein (1991), "Perfect codes in the metric of deletions and insertions", Diskretnaya Matematika, 3 (1): 3–20.
• VI Levenshtein, Designs as maximum codes in polynomial metric spaces, Acta Applicandae Mathematicae, vol. 29 (1992), 1-82.
• VI Levenshtein, Bounds for self-complementary codes and their applications, in Eurocode-92. CISM Courses and Lectures, vol. 339. Springer-Verlag, Wien-New-York, 1993, 159–171.
• VI Levenshtein, Bounds for codes as solutions of extremum problems for systems of orthogonal polynomials, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Lectures Notes in Computer Science, vol. 673, Springer-Verlag, 1993, 25–42.
• V.I. Levenshtein; A.J.H. Vinck (1993), "Perfect (d,k)-codes capable of correcting single peak-shifts", IEEE Transactions on Information Theory, 39 (2), IEEE: 656–662, Bibcode:1993ITIT...39..656L, doi:10.1109/18.212300
• V.I. Levenshtein (1993), "Packing and Decomposition Problems for Polynomial Association Schemes", European Journal of Combinatorics, 14 (5): 461–477, doi:10.1006/eujc.1993.1049
• T. Ericson and VI Levenshtein, Superimposed codes in the Hamming space, IEEE Trans. Inform. Theory, vol. 40, no. 6 (1994), 1882–1893.
• G. Fasekas and VI Levenshtein, On upper bounds for code distance and covering radius of designs in polynomial metric spaces, J. Combin. Th. Ser. A, vol. 70, no. 2 (1995), 267–288.
• T. Helleseth, T. Klove, VI Levenshtein, and O. Ytrehus, Bounds on the minimum support weights, IEEE Trans. Inform. Theory, vol. 41, no. 2 (1995), 432–440.
• VI Levenshtein, Krawtchouk polynomials and universal bounds for codes and designs in Hamming spaces, IEEE Trans. Inform. Theory, vol. 41, no. 5 (1995), 1303–1321.
• V.I. Levenshtein (1995), "A Simple Proof of the Basic Inequalities for the Fundamental Parameters of Codes in Polynomial Relationship Schemes", Problemy Peredachi Informatsii, 31 (4): 37–50.
• VI Levenshtein, Reconstructing binary sequences by the minimum number of their subsequences or supersequences of a given length. Proceedings of Fifth Intern. Workshop on Algebr. and Combin. Coding Theory, Sozopol, Bulgaria, June 1–7, 1996, 176–183.
• VI Levenshtein, Lower bounds on crosscorrelation of codes. Proceedings of IEEE Fourth Intern. Symp on Spread Spectrum Techniques and Appl., Mainz, Germany, September 22–25, 1996, 657–661.
• VI Levenshtein, Split orthogonal arrays and maximum independent resilient systems of functions, Designs, Codes and Cryptography, vol. 12, no. 2 (1997), 131–160.
• T. Helleseth, T. Klove, and VI Levenshtein, On the information function of an error-correcting code, IEEE Trans. Inform. Theory, vol. 43, no. 2 (1997), pp. 549–557.
• V.I. Levenshtein (1997), "Reconstruction of objects from the minimum number of distorted patterns", Doklady Akademii Nauk SSSR, 354 (5): 593–596
• P. Delsarte and VI Levenshtein, Association schemes and coding theory, IEEE Trans. Inform. Theory, vol. 44, no. 6 (1998), 2477–2504.
• VI Levenshtein, Universal bounds for codes and designs, in Handbook of Coding Theory, VS Pless and WC Huffman, Eds., Amsterdam: Elsevier, vol. 1, 499–648, 1998.
• VI Levenshtein, On designs in compact metric spaces and a universal bound on their size, Discrete Mathematics, vol. 192 (1998), 251–271.
• VI Levenshtein, On the maximum T-wise independent systems of Boolean functions, Workshop on Coding and Cryptography, Paris, France, 1999, 367–370.
• VI Levenshtein, Equivalence of Delsarte's bounds for codes and designs in symmetric association schemes and some applications, Discrete Mathematics, vol. 197/198 (1999), 515–536.
• VI Levenshtein, New lower bounds on aperiodic crosscorrelation of binary codes, IEEE Trans. Inform. Theory, vol. 45, no. 1 (1999), 284–288.
• IN AND. Levenshtein, On designs in continuous unit cubes, Proceedings of the IV International Conference: Discrete models in the theory of control systems, Moscow State University, MAKS Press, 2000, 62–64.
• VI Levenshtein, Efficient reconstruction of sequences, IEEE Trans. Inform. Theory, vol. 47, no. 1 (2001), 2-22.
• VI Levenshtein, Efficient reconstruction of sequences from their subsequences or supersequences, Journal of Combin. Theory, Ser. A, vol. 93, no. 2 (2001), 310–332.
• T. Berger and VI Levenshtein, Asymptotical efficiency of two-stage testing, IEEE Trans. Inform. Theory, vol. 48, no. 7 (2002), 1741–1749.
• T. Berger and VI Levenshtein, Application of cover-free codes and combinatorial designs to two-stage testing, Discrete Applied Mathematics.
• T. Helleseth, T. Klove and VI Levenshtein, Hypercubic 4 and 5-designs from double-error-correcting BCH codes, Designs, Codes and Cryptography.
• VI Levenshtein, A universal bound for a covering in regular posets and its application to pool testing, Discrete Mathematics.
• Helleseth, Tor; Kløve, Torleiv; Levenshtein, Vladimir (2005), "Error-correction capability of binary linear codes", IEEE Transactions on Information Theory, 51 (4), IEEE: 1408–1423, Bibcode:2005ITIT...51.1408H, doi:10.1109/TIT.2005.844080, S2CID 17840890
• VI Levenshtein, Combinatorial problems motivated by comma-free codes, Discrete Mathematics.

• Association scheme
• Bose–Mesner algebra
• Levenshtein automaton
• Levenshtein coding