Updated: December 2003

 

Papers by

Michael A. Tsfasman

Books (author):

• Algebraic Geometry Codes: Basic Notions. - IUM-MCCME, Moscow, 2003, 540 pages (in Russian, with D.Yu.Nogin and S.G.Vladuts)
• Algebraic Geometry and Number Theory: Rational and Elliptic Curves. - MCCME, Moscow, 2001, 48 pages (In Russian, with V.V.Ostrik)
• Algebraic-Geometric Codes. - Kluwer Acad.Publ., 1991, xxiv+667 pages (With S.G.Vladuts)
• Del Pezzo Surfaces of Degree Four. - Memoires de la Societe Math. de France, Nouvelle serie, # 37, 1989, 112 pages (With B.E.Kunyavskii and A.N.Skorobogatov)

                               Books (editor):

• Collected Papers of J.-P.Serre (in Russian), IUM-MCCME, Moscow, v.1, 2002,  v.2, 2003
• Coding Theory and Algebraic Geometry. Springer  Lect.  Notes in Math., v. 1518, 1992 (editor, with H.Stichtenoth)
• Special issue on Algebraic Geometry Codes of IEEE Transactions on Information Theory, IEEE Trans. Info. Theory, v. 41:6, 1995 (invited editor, with G.Lachaud, J.Justesen and V.K.-W.Wei)

   Reviews:

• Infinite Global Fields and the Generalized Brauer-Siegel Theorem. - In: Fundamental Mathematics Today, Ten years of the Independent University of Moscow. - IUM-MCCME, Moscow, 2003, pp. 335-351 (in Russian, with S.G.Vladuts)
• Lectures on global fields, lattices, and codes. - Methods of discrete mathematics (Braunschweig, 1999), Quad. Mat., 5, Aracne, Rome, 1999, pp.145-183
• Geometric approach to higher weights. - IEEE Trans. Info. Theory, vol.41:6, 1995, pp.1564-1588 (with S.G.Vladuts)
• Algebraic curves and sphere packings. - Algebraic Geometry and Coding Theory - 4, de Gruyter, Berlin, 1996, pp.225-252
• Global fields, codes and sphere packings. - Journees Arithmetiques 1989. - "Asterisque", 1992, v.198-199-200, pp.373-396
• Algebraic-geometric codes and asymptotic problems. - Applied Algebra and Error-Correcting Codes. - Discr. Appl. Math., 1991, v.33 , pp.241-256
• Rational varieties: algebra, geometry, arithmetic. - Russian Math. Surveys, 1986, v.41:2, pp.51-116 (With Yu.I.Manin)

   Main papers:

• Schubert varieties, linear codes and enumerative combinatorics. - Preprint 2003-04, Institut de Math. de Luminy, 2003 (with S.R.Ghorpade)
• Infinite Global Fields and the Generalized Brauer-Siegel Theorem. - Moscow Mathematical Journal, 2002, vol. 2:2, pp.329-402 (with S.G.Vladuts)
• Asymptotically good quantum codes. - Physical Review A., 2001, vol. 63, pp.032311-1-5 (with A.Ashikhmin and S.Litsyn)
• Random Lattices and Random Sphere Packings: Typical Properties. - Moscow Mathematical Journal, 2001, vol. 1:1, pp.73-89 (with S.Shlosman)
• Formules explicites pour le nombre de points des varietes sur un corps fini. - J. Reine Angew. Math., 1997, v.493, pp.1-60 (in French, with G.Lachaud)
• Asymptotic properties of zeta-functions. - Algebraic Geometry, 7 - J. Math. Sci. (New York), 1997, v.84:5, pp.1445-1467 (with S.G.Vladuts)
• Codes for m-metric. - Problems Inform. Transmission, 1997, v.33:1, pp.45-52 (with M.Yu.Rosenbloom)
• Nombre de points des surfaces sur un corps fini. - Algebraic Geometry and Coding Theory, de Gruyter, Berlin, 1996, pp.209-224 (in French)
• The weight hierarchy of higher-dimensional Hermitian codes. - IEEE Trans.Info.Theory, 40:1, 1994, pp.275-278 (with J.W.P.Hirschfeld and S.G.Vladuts)
• Some remarks on the asymptotic number of points. - Coding Theory and Algebraic Geometry. - Lect.Notes in Math., 1992, v.1518, pp.178-192
• Curves with many points and multiplication in finite  fields. - Coding Theory and Algebraic Geometry. - Lect. Notes in Math., 1992, v.1518, pp.145-169 (With I.E.Sparlinskii and S.G.Vladuts)
• Spectra of linear codes and error probability of decoding. - Coding Theory and Algebraic Geometry. - Lect. Notes in Math., 1992, v.1518, pp.82-98 (With G.L.Katsman and S.G.Vladuts)
• Multiplicative lattices in global fields. - Invent.Math., 1990, v.101, pp.687-696 (With M.Yu.Rosenbloom)
• A remark on algebraic-geometric codes. - Contemp.Math., 1989, v.93, pp.197-199 (With G.L.Katsman)
• Arithmetic on singular Del Pezzo surfaces. - Proc. London Math. Soc., 1988, v.(3) 57, pp.25-87 (With D.Coray)
• Spectra of algebraic-geometric codes. - Probl. Inform. Transmission, 1987, v.23, pp.262-275 (With G.L.Katsman)
• Constructive high-dimensional sphere packings. - Duke Math. J., 1987, v.54, pp.147-161 (With S.N.Litsyn)
• Zero-cycles on rational surfaces and Neron-Severi tori. - Math. USSR Izv., 1985, v.24, pp.583-603 (With B.E.Kunjavskii)
• Modular curves and codes with polynomial construction complexity. - Probl. Info.Trans., 20, 1984, pp35-42 (With S.G.Vladuts and G.L.Katsman)
• Modular curves and codes with polynomial construction. - IEEE Trans. Inform. Theory, 1984, v.30, pp.353-355 (With S.G.Vladuts and G.L.Katsman)
• Modular curves, Shimura curves, and Goppa codes better than the Varshamov-Gilbert bound. - Math. Nachr., 1982, v.109, pp.21-28 (With S.G.Vladuts and T.Zink)

   Short notes:

• Introduction to the special issue on algebraic geometry codes. - IEEE Trans. Info. Theory, v. 41:6, 1995, pp.1545-1546 (with G.Lachaud, J.Justesen and V.K.-W.Wei)
• Algebraic-geometric codes. An introduction. - Algebraic Geometry and Coding Theory - 3, 1991. - Lect. Notes in Math.,  1992, v.1518, pp.1-3 (With H.Stichtenoth)
• Algebraic-geometric codes on curves of small genera. - Probl. Inform. Transmission, 1987, v.23, pp.34-38  (With A.M.Barg and G.L.Katsman)
• A note on lower bounds. - IEEE Trans.Info.Theory, 1986, v.32, pp.705-706 (With S.N.Litsyn)
• Combinatorics and geometry of Del Pezzo surfaces of degree 4. - Russian Math. Surveys, 1985, v.40:6, pp.131-132 (With B.E.Kunjavskii and A.N.Skorobogatov)
• Algebraic-geometric and number-theoretic packings of balls in R^N. - Russian Math. Surveys, 1985, v.40:2, pp.219-220 (With S.N.Litsyn)
• Arithmetic of singular Del Pezzo surfaces. - Russian Math. Surveys, 1983, v.38:6, pp.137-138
• On Goppa codes which are better than the Varshamov-Gilbert bound. - Probl.Info.Trans., 1982, v.18, pp.163-166
• On the Neron-Severi torus of a rational surface. - Russian Math. Surveys, 1982, v.37:4, pp.121-122 (With B.E.Kunjavskii)
• The arithmetic of conic bundles. - Russian Math. Surveys, 1982, v.37:2, pp.263-264
• Moduli of very special Abelian varieties. - Russian Math. Surveys, 1978, v.33:5, p.211

      Abstracts of talks:

• Classical varieties, codes and combinatorics. - In: Proc. 15th International Conf. on Formal Power Series and Algebraic Combinatorics (FPSAC-2003), Vadstena, Sweden, 2003 (with S.R.Ghorpade)
• Asymptotic Propetries of Global Fields. - In: Finite Fields with Applications to Coding Theory, Cryptography and Related Areas (eds. G.Mullen, H.Stichtenoth, H.Tapia-Recillas), Springer Verlag, 2002, pp.328-334
• Asymptotically Good Quantum Codes. - In: Arithmetic, Geometry and Coding Theory 8, 2001, scientific reports of CIRM, 1 p.
• Asymptotic Properties of Global Fields. - In: Fundamental Mathematics Today, Short abstract of talks, 2001, pp.37-39
• Algebraic geometry lattices and codes. - Algorithmic number theory (Talence, 1996) - Lect. Notes in Comp. Sci., v.1122, Springer, Berlin, 1996, pp.385-389
• Geometric approach to higher weights of codes and a problem in cryptography. - 1993 IEEE Info. Theory Workshop, Susono-shi, Shizuoka, Japan, 1993
• Decoding of algebraic-geometric codes. - 1993 IEEE International Symposium on Information Theory, San Antonio,   Texas, 1993
• Algebraic geometry constructions in coding theory. - Second joint Swedish-Soviet international workshop on information theory. Proceedings, 1985, p.46-50 (With S.I.Gelfand and S.G.Vladuts)
• Good algebraic-geometric codes. - The sixth international symposium on information theory. Abstracts of papers. Part 2, Moscow-Tashkent, 1984, p.259-261 (With S.G.Vladuts)
• Codes from modular curves. - International workshop "Convolutional codes; multi-user communication". Abstracts of   papers. - Sochi, 1983, p.213-217 (With S.G.Vladuts)

                         Introductions:

• To the Russian translation of S.Koutinho. Introduction to Number Theory: RSA algorithm, Postmarket, Moscow, 2001. 
• To Collected Papers of J.-P.Serre (in Russian), IUM-MCCME, Moscow, v.1, 2002
• Robert A. Minlos. - Moscow Mathematical Journal, 2001, vol.1, n.3, pp.305-306 (with Yu.Ilyashenko, V.Malyshev, S.Shlosman, Ya.Sinai)
• Ivan Georgievich Petrovskii. - Moscow Mathematical Journal, 2001, vol.1, n.4, pp.473-474 (with V.Arnold, Yu.Ilyashenko, A.Kirillov, S.Novikov, A.Sossinski)
• Sergei N. Artemov. - Moscow Mathematical Journal, 2001, vol.1, n.4, p.643 (with Yu.Ilyashenko, V.Shehtman)
• Yuri Ivanovich Manin. - Moscow Mathematical Journal, 2001, vol.2, n.2, p.201-202 (with V.Ginzburg, Yu.Ilyashenko, S.Vladuts)
• Alexander Belavin. - Moscow Mathematical Journal, 2003, vol.3, n.1, p.255 (with B.Feigin, Yu.Ilyashenko, S.Lando, A.Sossinsky, V.Vassiliev)
• Victor Buchstaber. - Moscow Mathematical Journal, 2003, vol.3, n.1, p.257 (Yu.Ilyashenko, I.Krichever, S.Novikov, V.Vassiliev)

                         Articles for general public:

• Optimistic Tragedy: an Essay on Our Science and Education.  - Annals of the Motherland, v.2, 2002, pp. 111-124 (in Russian)
• L'Universite independente de Moscou. - Gazette des Mathematiciens, n.95, janvier 2003, pp.69-78 (in French, with A.Sossinsky)