Webwork Exercises for Applied Discrete Structures

This first cell computes the parity check matrix from the generator matrix. You need to refer to this matrix when you get a syndrome in the next cell.

The parity check matrix isn't unique. It is any matrix with the property that \​(b\) is a code word if and only if \​(b P\) is equal to a row of zeros. If an error occured in position \​(k\) of the data, then the syndrome, \​(b P\), will be row \​(k\) of \​(P\).

You can use this cell to compute the syndrome for any sequence of seven bits. Just replace the list of seven zeros in line 7 with whatever data you have. After you've identified the syndrome and corrected each 7-tuple, you can discard the last three bits.

Once you've corrected all four 7-tuples, combine them into a sequence of 16 bits. This code below will convert that sequence into a base 10 number. Just replace the sequence of all 1's with your sequence