Asymptotic improvement of the Gilbert-Varshamov bound on the size of binary codes

@article{Jiang2004AsymptoticIO,
  title={Asymptotic improvement of the Gilbert-Varshamov bound on the size of binary codes},
  author={T. Jiang and A. Vardy},
  journal={IEEE Transactions on Information Theory},
  year={2004},
  volume={50},
  pages={1655-1664}
}
  • T. Jiang, A. Vardy
  • Published 2004
  • Mathematics, Computer Science
  • IEEE Transactions on Information Theory
  • Given positive integers n and d, let A/sub 2/(n,d) denote the maximum size of a binary code of length n and minimum distance d. The well-known Gilbert-Varshamov bound asserts that A/sub 2/(n,d)/spl ges/2/sup n//V(n,d-l), where V(n,d) = /spl sigma//sub i=0//sup d/(/sub i//sup n/) is the volume of a Hamming sphere of radius d. We show that, in fact, there exists a positive constant c such that A/sub 2/(n, d)/spl ges/c2/sup n//V(n,d-1)log/sub 2/V(n, d-1) whenever d/n/spl les/0.499. The result… CONTINUE READING
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