Analysis of information sources in references of the Wikipedia article "Generator matrix" in English language version.
Because the Hamming code is a linear code, it can be written compactly in terms of matrices as follows. The transmitted codeword is obtained from the source sequence by a linear operation,where is the generator matrix of the code... I have assumed that and are column vectors. If instead they are row vectors, then this equation is replaced by... I find it easier to relate to the right-multiplication (...) than the left-multiplication (...). Many coding theory texts use the left-multiplying conventions (...), however. ...The rows of the generator matrix can be viewed as defining the basis vectors.
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