Generatormatrix

In the coding theory is a generator matrix, and the matrix generator, a base for a linear code, which produces all possible code words. If the matrix G and the linear code C, then

The systematic form for a generator matrix

Where a k × k identity matrix and P of dimension k × r.

A generator matrix may be used to generate a parity check matrix of a code (and vice versa).

Equivalent codes

Codes C1 and C2 are equivalent (written C1 ~ C2), if the code can be generated from the other by the following two transformations

Equivalent codes have the same Hamming distance.

The generator matrices of equivalent codes can be generated through the following transformations: