Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A NEW UPPER BOUND FOR SINGLE ERROR-CORRECTING CODES

  • Kim, Jun-Kyo (FACULTY OF LIBERAL ARTS, MIRYANG NATIONAL UNIVERSITY)
  • Published : 2001.01.01
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Abstract

The purpose of this paper is to give an upper bound for A[n,4], the maximum number of codewords in a binary code of word length n with minimum distance 4 between codewords. We have improved upper bound for A[12k+11,4]. In this correspondence we prove $A[23,4]\leq173716$.

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References

  1. EEE Trans. Inform. Theory v.IT-26 Binary Codes with a Minimum Distance of Four M. R. Best
  2. EEE Trans. Inform. Theory v.IT-24 Boundary for Binary Codes of Lenfth Less Than 25 M. R. Best;A. E. Brouwer;F. J. MacWilliams;A. M. Odlyzko;N. J. A. Sloane
  3. Discrete Math. v.17 The Triply Shortened Binary Hamming Code is Optimal M. R. Best;A. E. Brouwer
  4. J. Comb. Theory v.5 Optimal Packings of $K_4$'s into a $K_n$ A. E. Brower
  5. Sphere Packings, Lattices and Groups J. H. Conway;N. J. A. Sloane
  6. Combinatorial Theory M. Hall, Jr
  7. IEEE Trans. Inform. Theory v.IT-17 On Upper Bounds for Unrestricted Binary Error-correcting Codes S. M. Johnson
  8. Discrete Math. v.187 A New upper Bounda for Binary Codes with Minimum Distance Four J. K. Lim;S. G. Hahn
  9. Cambridge adn Dublin Math. J. v.2 On a Problem in Combinations T. P. Kirkman
  10. Studia Sci. Math. Hungar v.1 On Maximal System of K-tuples J. Schonheim
  11. Discrete Math. v.3 Survey of Constructuve Coding Theory and a Table of Binary Codes of Highest Known Rate N. J. A. Sloane
  12. Combinatorial, Configurations, Designs, Codes, Graphs V. D. Tonchev