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Gardy and Sole provide a Gilbert-Varshamov lower bound and a Hamming upper bound for the Lee metric when the distance between codewords is smaller than the length of the code (captured by $r = \delta n$ where $0 \le \delta \le 0.37$ in the paper).

Is there a reference which provides the corresponding lower/upper bound for ranges above this? At least is there a lower bound (preferably as powerful as the Gilbert-Varshamov bound) and a upper bound(preferably tighter than the Hamming bound) for the case $\frac{2 \delta n + 1}{n} = \frac{n + 1}{n}$, that is $\delta = \frac{1}{2}$?

This is a smaller version of the cross-posting from MO.

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  • $\begingroup$ Closed for simultaneous cross-posting on MO. If you don't get an answer on MO after a few days, flag the post and we will reopen it. $\endgroup$
    – Kaveh
    Commented Jul 16, 2011 at 22:37
  • $\begingroup$ @Kaveh ok Thankyou $\endgroup$
    – v s
    Commented Jul 17, 2011 at 0:13

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