Systematic code

A systematic code is a code that k assigns to each message word length of a code word of length n, where the message word explicitly part of the associated codeword.

As an example, parity tests, where the message word one or more check bits are appended apply.

Definition

A systematic code is an (n, k) linear code such that the first k digits of the code words from the original message placement units and the other m = n - k points are taken as control points.

Example

A systematic [n, k] code can look like this: . This code could be described by the following function: . And in particular, we have:

Now we have a systematic in k digits code of length n with minimum distance d ( Hamming distance ) and can also write.

• Encoding