Properties
Every non-systematic linear code can be transformed into a systematic code with essentially the same properties (i.e., minimum distance). Because of the advantages cited above, linear error-correcting codes are therefore generally implemented as systematic codes. However, for certain decoding algorithms such as sequential decoding or maximum-likelihood decoding, a non-systematic structure can increase performance in terms of undetected decoding error probability when the minimum free distance of the code is larger.
For a systematic linear code, the generator matrix, can always be written as, where is the identity matrix of size .
Read more about this topic: Systematic Code
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—Ralph Waldo Emerson (1803–1882)
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