##  [Gilbert–Varshamov Bound](/gilbert-varshamov-bound) 

  ##  [Gilbert–Varshamov Bound](https://information.quantumdictionary.io/gilbert-varshamov-bound-0) 

  

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**Information & Communication Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An existential lower bound on the maximum size M of a q-ary block code of length n and minimum Hamming distance d: there exists a code with at least M ≥ q^n / V_q(n,d-1) codewords, where V_q(n,d-1)=∑_{i=0}^{d-1} binom(n,i)(q-1)^i (equivalently derived via a greedy construction). The bound guarantees existence (but not efficient constructibility) of codes meeting these parameters.