A maximum distance separable code, abbreviated MDS code, is a code attaining the Singleton bound. A linear
code over a finite field, of length 
and dimension 
with 
,
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).
Maximum Distance Separable Code
See also
Coding Theory, Generator Matrix, Hamming Distance, Linear Code, MDS Conjecture, Singleton BoundExplore with Wolfram|Alpha
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