生成矩阵 (Chinese Wikipedia)

Analysis of information sources in references of the Wikipedia article "生成矩阵" in Chinese language version.

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cam.ac.uk

MacKay, David, J.C. Information Theory, Inference, and Learning Algorithms (PDF). Cambridge University Press. 2003: 9. ISBN 9780521642989. Because the Hamming code is a linear code, it can be written compactly in terms of matrices as follows. The transmitted codeword $\mathbf {t}$ is obtained from the source sequence $\mathbf {s}$ by a linear operation,
$\mathbf {t} =\mathbf {G} ^{\intercal }\mathbf {s}$
where $\mathbf {G}$ is the generator matrix of the code... I have assumed that $\mathbf {s}$ and $\mathbf {t}$ are column vectors. If instead they are row vectors, then this equation is replaced by
$\mathbf {t} =\mathbf {sG}$
The rows of the generator matrix can be viewed as defining the basis vectors.