Singleton bound#MDS codes

MDS code is the abbreviation for Maximum Distance Separable code, the German term is maximum distance code.

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

The coding theory (in particular error correction codes) are primarily of interest codes in which the code words are so far apart as possible. The distance between two code words the Hamming distance. The minimum distance of a code is the minimum distance between two code words. This distance is to be maximized.

Leads to the definition of maximum distance code, Be is a linear code (length, dimension, minimum distance ). have continued the property. Then is called a separable maximum distance code ( MDS ) code. That is an MDS code satisfies the Singleton bound with equality. He is further characterized in that arbitrary positions make the code words clearly distinguishable from each other.

For binary codes exist only the following trivial MDS codes:

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

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

• Coding Theory