Generator Matrix

Given a linear code C, a generator matrix G of C is a matrix whose rows generate all the elements of C, i.e., if G=(g_1 g_2 ... g_k)^(T), then every codeword w of C can be represented as


in a unique way, where c=(c_1 c_2 ... c_k).

An example of a generator matrix is the Golay code, which consists of all 2^(12) possible binary sums of the 11 rows.

See also

Coding Theory, Error-Correcting Code, Linear Code, Parity Check Matrix

Portions of this entry contributed by David Terr

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Roman, S. Coding and Information Theory. New York: Springer-Verlag, 1992.van Lint, J. H. An Introduction to Coding Theory, 2nd ed. New York: Springer-Verlag, 1992.

Referenced on Wolfram|Alpha

Generator Matrix

Cite this as:

Terr, David and Weisstein, Eric W. "Generator Matrix." From MathWorld--A Wolfram Web Resource.

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