Gilbert–Varshamov bound for linear codes

The Gilbert–Varshamov bound for linear codes is related to the general Gilbert–Varshamov bound, which gives a lower bound on the maximal number of elements in an error-correcting code of a given block length and minimum Hamming weight over a field F q {\displaystyle \mathbb {F} _{q}} . This may be translated into a statement about the maximum rate of a code with given length and minimum distance.