A systematic code is a code which assigns a code word of length n to each message word of length k , the message word being explicitly part of the assigned code word.
As an example, apply parity checks in which the message word one or more check bits are appended.
example
A systematic [n, k] code can look like this: . This code could be achieved by following function describe: . And in detail we would have:
, , , .
Now we have a systematic in k point code of length n with minimum distance d ( Hamming distance ) and can also write: .