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Two new bounds on the size of binary codes with a minimum distance of three

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We prove two new upper bounds on the size of binary codes with a minimum distance of three, namelyA(10, 3)≤76 andA(11, 3)≤152.

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References

  1. J. L. Allston, R. W. Buskens, and R. G. Stanton, An examination of the nonisomorphic solutions to a problem in covering designs in fifteen points.Math. Comp., Vol. 4 (1988) pp. 189–206.

    Google Scholar 

  2. M. R. Best, Binary codes with a minimum distance of four,IEEE Trans. Inform. Theory, Vol. IT-26 (1980) pp. 738–742.

    Google Scholar 

  3. M. R. Best, A. E. Brouwer, F. J. MacWilliams, A. M. Odlyzko, and N. J. A. Sloane, Bounds for binary codes of length less than 25,IEEE Trans. Inform. Theory, Vol. IT-24 (1978) pp. 81–93.

    Google Scholar 

  4. J. H. Conway and N. J. A. Sloane,Sphere Packings, Lattices and Groups, Springer-Verlag, New York (1988).

    Google Scholar 

  5. J. H. Conway and N. J. A. Sloane, Quaternary constructions for the binary codes of Julin, Best, and others,Designs, Codes, and Cryptography, to appear.

  6. D. Julin, Two improved block codes.IEEE Trans. Inform. Theory, Vol. IT-11 (1965) p. 459.

    Google Scholar 

  7. D. E. Knuth,The Art of Computer Programming: Sorting and Searching, Addison-Wesley, Reading, MA (1973).

    Google Scholar 

  8. S. Litsyn and A. Vardy, The uniqueness of the Best code,IEEE Trans. Inform. Theory. to appear.

  9. F. J. MacWilliams and N. J. A. Sloane,The Theory of Error-Correcting Codes, North-Holland, New York (1977).

    Google Scholar 

  10. N. Wax, On upper bounds for error-detecting and error-correcting codes of finite length.IEEE Trans. Inform. Theory, Vol. IT-5 (1959) pp. 168–174.

    Google Scholar 

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Communicated by: D. Jungnickel

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Klein, Y., Litsyn, S. & Vardy, A. Two new bounds on the size of binary codes with a minimum distance of three. Des Codes Crypt 6, 219–227 (1995). https://doi.org/10.1007/BF01388476

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  • DOI: https://doi.org/10.1007/BF01388476

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