A Griesmer code is a linear code attaining equality in the Griesmer bound. Thus an ![[n,k,d]_q](/images/equations/GriesmerCode/Inline1.svg)
Griesmer code has ![n=sum_(i=0)^(k-1)[d/q^i]](/images/equations/GriesmerCode/Inline2.svg)
, where ![[x]](/images/equations/GriesmerCode/Inline3.svg)
is the ceiling function.
The divisibility of the Hamming weights of their codewords is addressed by Ward's
conjecture, proved by Deng and Zhang (2026).
See also
Griesmer Bound,
Hamming
Weight,
Linear Code
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References
Deng, H. and Zhang, W. "A Proof of Ward's Conjecture on Griesmer Codes." 21 Oct 2026. https://arxiv.org/abs/2610.29275.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 Code." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GriesmerCode.html
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