
Section15.5Section 15-5 Coding

SubsectionExercises

1

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

WeBWorK Exercise