A partity check can be represented as a form of matrix multiplication.
Imagine we have an input bit stream, a, of length k:
Then a matrix of the form below will perform an even parity check if k is odd (or an odd parity check if k is even):
Here’s a very simple worked example:
Let a = 10110
Parity check matrix =
Output = 101101 (modulo 2 arithmetic is used to compute each ‘column’ in the output)
Of course parity checks are a crude form of 1 bit error detection and do not allow for error correction.