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A family of binary codes with asymptotically good distance distribution

  • Section 1 Algebraic Codes
  • Conference paper
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EUROCODE '90 (EUROCODE 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 514))

Abstract

After proving that long binary block codes having the same error exponent as optimum codes (those that attain the minimum possible probability of error) have binomial distance distribution, an infinite sequence of even self-dual codes based on Hadamard matrices is constructed that is conjectured to satisfy the requirements. The first two codes in the sequence are the extended Hamming [8,4,4] and Golay [24,12,8] codes.

T. Beth is with Universität Karlsruhe, Fakultät für Informatik, Institut für Algorithmen und Kognitive Systeme, Am Fasanengarten 5 (Geb. 5034), D-7500 Karlsruhe, FR Germany.

D.E.Lazić is with Universität Karlsruhe, Fakultät für Informatik, Institut für Algorithmen und Kognitive Systeme, Am Fasanengarten 5 (Geb. 5034), D-7500 Karlsruhe, FR Germany, Alexander von Humboldt Fellow, on leave from Faculty of Technical Sciences, Computer Science, Control and Measurements Institute, V. Vlahovica 3, 21000 Novi Sad, Yugoslavia.

V.Šenk is with Faculty of Technical Sciences, Computer Science, Control and Measurements Institute, V. Vlahovica 3, 21000 Novi Sad, Yugoslavia.

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References

  1. C.E. Shannon: "A Mathematical Theory of Communications", BSTJ, 27, pp. 379–423 and 623–656, 1948.

    Google Scholar 

  2. F.J. MacWilliams, N.J.A. Sloane: "The Theory of Error Correcting Codes", Part I and II, North-Holland, 1977.

    Google Scholar 

  3. R. E. Blahut: "Principles and Practice of Information Theory", Addison-Wesley, 1987.

    Google Scholar 

  4. R.G. Gallager: "Information Theory and Reliable Communication", John Willey and Sons, 1968.

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  5. J.N. Pierce: "Limit Distributions of the Minimum Distance of Random Linear Codes", IEEE Transactions on Information Theory, Vol IT-13, No.4, pp.595–599, October 1967.

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  6. T. Beth: "Codes und Invarianten" in "Mathematishes Codierung Theorie", Erlangen 1978.

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  7. D.E. Lazić, V. Šenk: "A Simple Geometrical Method for Determination of the Error Exponent for Deterministic Channel Block Codes — Part I: Cutoff Rate Bound, and Part II: the Tight Solution", submitted to IEEE Transactions on Information Theory, 1990.

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  8. G. Battail: "Construction explicite de Bons Codes Longs", Ann. Telecommun., 44,No. 7–8, pp.392–404, 1989.

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Authors
  1. T. Beth
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  2. D. E. Lazić
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  3. V. Šenk
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Editor information

Gérard Cohen Pascale Charpin

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© 1991 Springer-Verlag Berlin Heidelberg

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Beth, T., Lazić, D.E., Šenk, V. (1991). A family of binary codes with asymptotically good distance distribution. In: Cohen, G., Charpin, P. (eds) EUROCODE '90. EUROCODE 1990. Lecture Notes in Computer Science, vol 514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54303-1_115

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  • DOI: https://doi.org/10.1007/3-540-54303-1_115

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54303-9

  • Online ISBN: 978-3-540-47546-0

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