Parity Check Matrix

Given a linear code C of length n and dimension k over the field F, a parity check matrix H of C is a n×(n-k) matrix whose rows generate the orthogonal complement of C, i.e., an element w of F^n is a codeword of C iff wH=0. The rows of H generate the null space of the generator matrix G.

See also

Coding Theory, Error-Correcting Code, Generator Matrix, Linear Code

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.

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Parity Check Matrix

Cite this as:

Terr, David. "Parity Check Matrix." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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