Improved sphere bounds on the covering radius of codes

  • Authors:

  • G. J.M. van Wee

  • Affiliations:

  • Dept. of Math. & Comput. Sci., Eindhoven Univ. of Technol.

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

The sphere bound is a trivial lower bound on K(n,R), the minimal cardinality of any binary code of length n and with covering radius R. By simple arguments it is considerably improved, to K(n,1)⩾2 n/n for n even. A table of lower and upper bounds on K(n,R) for n⩽33, R ⩽10 is included