Maximum Distance Separable Code

A maximum distance separable code, abbreviated MDS code, is a code attaining the Singleton bound. A linear code of length and dimension is maximum distance separable when its minimum Hamming distance is . Equivalently, every selection of columns of a generator matrix is linearly independent. The MDS conjecture concerns the largest possible length of these linear codes over a finite field (Fan 2026).

See also

Hamming Distance, Linear Code, MDS Conjecture, Singleton Bound

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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. "Maximum Distance Separable Code." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MaximumDistanceSeparableCode.html

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