The Griesmer bound is a lower bound on the length 
of a linear code of dimension 
and minimum Hamming
distance 
over the finite field 
:
![n>=g_q(k,d)=sum_(i=0)^(k-1)[d/q^i].](/images/equations/GriesmerBound/NumberedEquation1.svg) |
Here ![[x]](/images/equations/GriesmerBound/Inline5.svg)
is the ceiling function. A code attaining equality
is a Griesmer code (Deng and Zhang 2026).
Griesmer Bound
See also
Griesmer Code, Hamming Distance, Linear CodeExplore with Wolfram|Alpha
References
Deng, H. and Zhang, W. "A Proof of Ward's Conjecture on Griesmer Codes." 21 Oct 2026. https://arxiv.org/abs/2610.29275.Griesmer, J. H. "A Bound for Error-Correcting Codes." IBM J. Res. Develop. 4, 532-542, 1960. https://doi.org/10.1147/rd.45.0532.Huffman, W. C. and Pless, V. Fundamentals of Error-Correcting Codes. Cambridge, England: Cambridge University Press, 2003. https://doi.org/10.1017/CBO9780511807077.Cite this as:
Weisstein, Eric W. "Griesmer Bound." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GriesmerBound.html