Given a linear code 
of length 
and dimension 
over the field 
, a parity check matrix 
of 
is a 
matrix whose rows generate the orthogonal complement
of 
,
i.e., an element 
of 
is a codeword of 
iff 
. The rows of 
generate the null space of the
generator matrix 
.
Parity Check Matrix
See also
Coding Theory, Error-Correcting Code, Generator Matrix, Linear CodeThis entry contributed by David Terr
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References
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
Parity Check MatrixCite this as:
Terr, David. "Parity Check Matrix." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ParityCheckMatrix.html