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To take into account the possibility of errors, you can also remark that you can fix the value of other variables to any value. So instead of doing the sum only once for other variables not in <math display="inline"> \mu </math> with 0 value, you do it <math display="inline"> 2^{m-d} </math> times for each fixed valuations of the other variables. If there is no error, all those sums should be equals to the value of the coefficient searched.
The algorithm consists here to take the majority of the answers as the value searched. If the minority is larger than the maximum number of errors possible, the decoding step fails knowing there are too
Once a coefficient is computed, if it's 1, update the code to remove the monomial <math display="inline"> \mu </math> from the input code and continue to next monomial, in reverse order of their degree.
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