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This article needs attention from an expert on the subject. See the talk page for details. WikiProject Technology or the Technology Portal may be able to help recruit an expert. (February 2010) In coding theory, a parity-check matrix of a linear block code C is a generator matrix of the dual code. As such, a codeword c is in C if and only if the matrix-vector product Hc=0. The rows of a parity check matrix are parity checks on the codewords of a code. That is, they show how linear combinations of certain digits of each codeword equal zero. For example, the parity check matrix specifies that for each codeword, digits 1 and 2 should sum to zero (according to the second row) and digits 3 and 4 should sum to zero (according to the first row). Creating a parity check matrix The parity check matrix for a given code can be derived from its generator matrix (and vice-versa). If the generator matrix for an [n,k]-code is in standard form , then the parity check matrix is given by , because GHT = P − P = 0. Negation is performed in the finite field mod q. Note that if the characteristic of the underlying field is 2 (i.e., 1 + 1 = 0 in that field), as in binary codes, then − P = P, so the negation is unnecessary. For example, if a binary code has the generator matrix The parity check matrix becomes For any valid codeword x, Hx = 0. For any invalid codeword , the syndrome S satisfies . See also Hamming code References Hill, Raymond (1986). A first course in coding theory. Oxford Applied Mathematics and Computing Science Series. Oxford University Press. pp. 69. ISBN 0-19-853803-0.  Pless, Vera (1982). Introduction to the theory of error-correcting codes. Wiley-Interscience Series in Discrete Mathematics. John Wiley & Sons. pp. 8. ISBN 0-471-08684-3.  J.H. van Lint (1992). Introduction to Coding Theory. GTM. 86 (2nd ed ed.). Springer-Verlag. pp. 34. ISBN 3-540-54894-7.  This mathematics-related article is a stub. You can help Wikipedia by expanding it.v · d · e