MDS code

MDS code is the abbreviation for Maximum Distance Separable Code , the German name is Maximum Distance Code .

An MDS code is a special case of the block codes used in channel coding .

In coding theory (in particular error correction codes), codes of particular interest are those in which the code words are as far apart as possible. The distance between two code words is the Hamming distance . The minimum distance of a code is the minimum distance between two different code words. It is important to maximize this distance.

This leads to the definition of maximum distance codes: Let a linear code (length  , dimension  , minimum distance  ). still have the property . Then a separable maximum distance code (MDS code) is called. That is, an MDS code fulfills the singleton limit with equality. It is further characterized by the fact that arbitrary  positions make the code words clearly distinguishable from one another. ${\displaystyle C}$ ${\displaystyle (n,k,d)}$ ${\displaystyle n}$ ${\displaystyle k}$ ${\displaystyle d}$ ${\displaystyle C}$ ${\displaystyle d=n-k+1}$ ${\displaystyle C}$ ${\displaystyle k}$

Only the following trivial MDS codes exist for binary codes:

• Repeat code
• 1-bit parity check code
• Code without redundancy

An example of a non-binary MDS code is the Reed-Solomon code .