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.

  • $\begingroup$ 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


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.