Singleton Bound

The Singleton bound states that a code of length over an alphabet of size , with minimum Hamming distance , satisfies

Deleting any coordinates maps distinct codewords to distinct words, which proves the bound. For a linear code of dimension , it becomes . A code attaining equality is a maximum distance separable code (Fan 2026).

See also

Code, Hamming Distance, Linear Code, Maximum Distance Separable Code, MDS Conjecture

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References

Fan, X. "A Linear-in-

Range of Dimensions for the MDS Conjecture over

in Odd Characteristic." 22 Sep 2026. https://arxiv.org/abs/2610.03740.

Cite this as:

Weisstein, Eric W. "Singleton Bound." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SingletonBound.html

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