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Vladimir Levenshtein

December 13, 2023

Vladimir Iosifovich Levenshtein (Russian: Влади́мир Ио́сифович Левенште́йн, IPA: [vlɐˈdʲimʲɪr ɨˈosʲɪfəvʲɪtɕ lʲɪvʲɪnˈʂtʲejn] ⓘ; 20 May 1935 – 6 September 2017) was a Russian and Soviet scientist who did research in information theory, error-correcting codes, and combinatorial design.[1] Among other contributions, he is known for the Levenshtein distance and a Levenshtein algorithm, which he developed in 1965.

Vladimir Levenshtein
Born
Vladimir Iosifovich Levenshtein

(1935-05-20)20 May 1935
Moscow, USSR
Died6 September 2017(2017-09-06) (aged 82)
NationalityRussian
CitizenshipRussia
Alma materMoscow State University
Known forLevenshtein distance
Levenshtein automaton
Levenshtein coding
AwardsIEEE Richard W. Hamming Medal (2006)
Scientific career
FieldsMathematics
InstitutionsKeldysh Institute of Applied Mathematics

He graduated from the Department of Mathematics and Mechanics of Moscow State University in 1958 and worked at the Keldysh Institute of Applied Mathematics in Moscow ever since. He was a fellow of the IEEE Information Theory Society.

He received the IEEE Richard W. Hamming Medal in 2006, for "contributions to the theory of error-correcting codes and information theory, including the Levenshtein distance".[2]

Life edit

Levenshtein graduated from Moscow State University in 1958, where he studied in the faculty of Mechanics and Mathematics. After graduation he worked at the M.V Keldysh Institute of Applied Mathematics.

Publications edit

  • 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, 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, IEEE, 39 (2): 656–662, 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, IEEE, 51 (4): 1408–1423, doi:10.1109/TIT.2005.844080, S2CID 17840890
  • VI Levenshtein, Combinatorial problems motivated by comma-free codes, Discrete Mathematics.

See also edit

References edit

  1. ^ "Код без ошибок". nplus1.ru (in Russian). Retrieved 2017-10-21.
  2. ^ "IEEE Richard W. Hamming Medal Recipients" (PDF). IEEE. Retrieved May 29, 2011.

External links edit

  • Levenshtein's personal webpage - in Russian
  • March 2003 pictures of Levenshtein at a professional reception.
  • Another (better) picture from the same source
  • . IEEE. Archived from the original on 2007-09-19.

December 13, 2023
vladimir, levenshtein, vladimir, iosifovich, levenshtein, russian, Влади, мир, Ио, сифович, Левенште, йн, vlɐˈdʲimʲɪr, ɨˈosʲɪfəvʲɪtɕ, lʲɪvʲɪnˈʂtʲejn, 1935, september, 2017, russian, soviet, scientist, research, information, theory, error, correcting, codes, co. Vladimir Iosifovich Levenshtein Russian Vladi mir Io sifovich Levenshte jn IPA vlɐˈdʲimʲɪr ɨˈosʲɪfevʲɪtɕ lʲɪvʲɪnˈʂtʲejn 20 May 1935 6 September 2017 was a Russian and Soviet scientist who did research in information theory error correcting codes and combinatorial design 1 Among other contributions he is known for the Levenshtein distance and a Levenshtein algorithm which he developed in 1965 Vladimir LevenshteinBornVladimir Iosifovich Levenshtein 1935 05 20 20 May 1935Moscow USSRDied6 September 2017 2017 09 06 aged 82 NationalityRussianCitizenshipRussiaAlma materMoscow State UniversityKnown forLevenshtein distanceLevenshtein automatonLevenshtein codingAwardsIEEE Richard W Hamming Medal 2006 Scientific careerFieldsMathematicsInstitutionsKeldysh Institute of Applied MathematicsHe graduated from the Department of Mathematics and Mechanics of Moscow State University in 1958 and worked at the Keldysh Institute of Applied Mathematics in Moscow ever since He was a fellow of the IEEE Information Theory Society He received the IEEE Richard W Hamming Medal in 2006 for contributions to the theory of error correcting codes and information theory including the Levenshtein distance 2 Contents 1 Life 2 Publications 3 See also 4 References 5 External linksLife editLevenshtein graduated from Moscow State University in 1958 where he studied in the faculty of Mechanics and Mathematics After graduation he worked at the M V Keldysh Institute of Applied Mathematics Publications editLevenshtein 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 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 IEEE 39 2 656 662 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 Klove Torleiv Levenshtein Vladimir 2005 Error correction capability of binary linear codes IEEE Transactions on Information Theory IEEE 51 4 1408 1423 doi 10 1109 TIT 2005 844080 S2CID 17840890 VI Levenshtein Combinatorial problems motivated by comma free codes Discrete Mathematics See also editAssociation scheme Bose Mesner algebra Levenshtein automaton Levenshtein codingReferences edit Kod bez oshibok nplus1 ru in Russian Retrieved 2017 10 21 IEEE Richard W Hamming Medal Recipients PDF IEEE Retrieved May 29 2011 External links editLevenshtein s personal webpage in Russian March 2003 pictures of Levenshtein at a professional reception Another better picture from the same source 2006 Richard W Hamming Medal IEEE Archived from the original on 2007 09 19 Retrieved from https en wikipedia org w index php title Vladimir Levenshtein amp oldid 1182828290, wikipedia, wiki, book, books, library,

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