Abstract
Some classical bounds are derived and discussed in a unified manner, along with a few more recent results.
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F.J. MacWilliams and N.J.A. Sloane, "The theory of error-correcting codes", North Holland, 1977
J.H. van Lint, "Introduction to coding theory", Graduate texts in mathematics, vol. 86, New York: Springer Verlag, 1982
Th. Beth, D. Jungnickel and H. Lenz, "Design theory", Wissenschaftsverlag, Mannheim, Wien, Zürich, 1985
E.M. Gilbert, "A comparison of signalling alphabets", Bell syst. techn. journal, vol. 31, pp. 504–522, 1952
R.R. Varshamov, "Estimate of the number of signals in error-correcting codes", Dokl. Akad. Nank SSSR, vol. 117, pp. 739–741, 1957
E.L. Blokh and V.V. Zyablov, "Linear concatenated codes", Moscow 1982, (in Russian)
R.J. McEliece, E.R. Rodemich, H.C. Rumsey, Jr. and L.R. Welch, "New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities", IEEE Trans. Info. Theory, vol. IT-23, pp. 157–166, 1977
M.A. Tsfasman, S.G. Vladut and Th. Zink, "Modular curves, Shimura curves and Goppa codes, better than Varshamov-Gilbert bound", Math. Nachr., vol. 104, pp. 13–28, 1982
V.D. Goppa, "Codes on algebraic curves", Soviet Math. Doklady, vol. 24, pp. 170–172, 1981
V.D. Goppa, "Algebraic geometry codes", Math. USSR Isvestiga, vol. 21, pp. 75–91, 1983
G.L. Katsman, M.A. Tsfasman and S.G. Vladut, "Modular curves and codes with a polynomial construction", IEEE Trans. Info. Theory, vol. IT-30, pp. 353–355, 1984
M.A. Tsfasman, "Goppa codes that are better than the Varshamov-Gilbert bound", Probl. of Info. Transm., vol. 18, pp. 163–165, 1982
J.H. van Lint and T.A. Springer, "Generalized Reed-Solomon codes from algebraic geometry", IEEE Trans. Info. Theory, vol. IT-33, pp. 305–309, May 1987
V.I. Levenshtein, "Upper bound estimates for fixed-weight codes", Probl. of Info. Transm., vol. 7, pp. 281–287, (Engl. transl.), 1971
V.I. Levenshtein, "Minimum redundancy of binary error-correcting codes", Probl. of Info. Transm., vol. 10, pp. 110–123, (Engl. transl.), 1974
V.M. Sidelnikov, "Upper bounds for the number of points of a binary code with a specified code distance", Probl. of Info. Transm., vol. 10, pp. 124–131 (Engl. transl.), 1974
L.A. Bassalygo, "New upper bounds for error-correcting codes", Probl. of Info. Transm., vol. 1, pp. 32–35 (Engl. transl.), 1965
T. Ericson and V.V. Zinoviev, "An improvement of the Gilbert bound for constant weight codes", IEEE Trans. Info. Theory, vol. IT-33, pp. 720–723, September 1987
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© 1989 Springer-Verlag
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Ericson, T. (1989). Bounds on the size of a code. In: Einarsson, G., Ericson, T., Ingemarsson, I., Johannesson, R., Zigangirov, K., Sundberg, C.E. (eds) Topics in Coding Theory. Lecture Notes in Control and Information Sciences, vol 128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042067
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DOI: https://doi.org/10.1007/BFb0042067
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