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International Conference on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes

AAECC 1984: Applied Algebra, Algorithmics and Error-Correcting Codes pp 90–106Cite as

An improved upper bound on covering radius

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 228))

Abstract

A simple upper bound on covering radius yields new information on various codes. It leads us to show that the nonlinear codes of Sloane and Whitehead [18] are quasi-perfect. We get some new bounds for the Berlekamp-Gale switching problem [7]. It gives the exact covering radius for some codes of length up to 31 and is within 1 or 2 of the exact value for the even quadratic-residue codes of lengths 41 and 47.

Part of this paper was presented at the Fourth Caribbean Conference on Combinatorics and Computing, San Juan, April 1–4, 1985.

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References

  1. E. F. Assmus, Jr., and Vera Pless, “On the covering radius of extremal self-dual codes,” IEEE Trans. Inform. Theory, IT-29 (1983) 359–363.

    Google Scholar 

  2. E. R. Berlekamp Algebraic Coding Theory, McGraw Hill, New York, 1968.

    Google Scholar 

  3. Gérard D. Cohen, Mark R. Karpovsky, H. F. Mattson, Jr., and James R. Schatz, “Covering Radius—Survey and Recent Results,” IEEE Trans. Inform. Theory IT-31 (1985), 328–343.

    Google Scholar 

  4. Ph. Delsarte, “Four fundamental parameters of a code and their combinatorial significance,” Inform. and Control 23 (1973), 407–438.

    Google Scholar 

  5. Diane E. Downey and N. J. A. Sloane, “The covering radius of cyclic codes of length up to 31,” IEEE Trans. Inform. Theory, IT-31 (1985), 446–447.

    Google Scholar 

  6. M. J. E. Golay, “Binary coding,” IEEE Trans. Inform. Theory, PGIT-4 (1954) 23–28.

    Google Scholar 

  7. R. L. Graham and N. J. A. Sloane, “On the covering radius of codes,” IEEE Trans. Inform. Theory, IT-31 (1985), 385–401.

    Google Scholar 

  8. J. H. Griesmer, “A bound for error-correcting codes,” IBM J. Res. Develop. 4 (1960), 532–542.

    Google Scholar 

  9. H. J. Helgert and R. D. Stinaff, “Minimum-distance bounds for binary linear codes,” IEEE Trans. Inform. Theory IT-19 (1973), 344–356.

    Google Scholar 

  10. D. Julin, “Two improved block codes,” IEEE Trans. Inform. Theory, IT-11 (1965) 459.

    Google Scholar 

  11. Mark R. Karpovsky, public communication, at Journée sur le rayon de recouvrement et codes correcteurs d'érreurs, ENST, Paris, 26 June 1984.

    Google Scholar 

  12. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North Holland, Amsterdam, 1977.

    Google Scholar 

  13. H. F. Mattson, Jr., “An upper bound on covering radius,” Annals of Discrete Math. 17 (1982) 453–458.

    Google Scholar 

  14. H. F. Mattson, Jr. “Another upper bound on covering radius,” IEEE Trans. Inform. Theory, IT-29 (1983) 356–359.

    Article  Google Scholar 

  15. W. W. Peterson and E. J. Weldon, Jr., Error-correcting codes, Second Edition, Cambridge, M.I.T. 1972.

    Google Scholar 

  16. V. Pless and E. A. Prange, “Weight distribution of all cyclic codes ... [of length] 31 over GF(2)” unpublished memorandum, September, 1962.

    Google Scholar 

  17. James R. Schatz, “On the coset leaders of Reed-Muller codes,” Ph. D. dissertation, Syracuse University, 1979.

    Google Scholar 

  18. Neil J. A. Sloane and Donald S. Whitehead, “New family of single-error correcting codes, IEEE Trans. Inform. Theory, IT-16 (1970) 717–719.

    Google Scholar 

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Authors and Affiliations

  1. School of Computer and Information Science, Syracuse University, 13244-1240, Syracuse, N.Y.

    H. F. Mattson Jr.

Authors
  1. H. F. Mattson Jr.
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Alain Poli

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© 1986 Springer-Verlag Berlin Heidelberg

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Mattson, H.F. (1986). An improved upper bound on covering radius. In: Poli, A. (eds) Applied Algebra, Algorithmics and Error-Correcting Codes. AAECC 1984. Lecture Notes in Computer Science, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16767-6_53

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  • DOI: https://doi.org/10.1007/3-540-16767-6_53

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16767-9

  • Online ISBN: 978-3-540-38813-5

  • eBook Packages: Springer Book Archive

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