have reached polynomial of degree at most 3, and as we get Therefore, Let Don't worry that The root of is Let Let us look for error values using formula where are roots of polynomial We get The fact that should not be surprising. Corrected code is therefore [ 1 0 1 1 0 0 0 1 0 1 0 0]. Citations References Primary sources Secondary sources Course notes are apparently being redone for 2012: http://www.stanford.edu/class/ee387/ Further reading Error detection and correction Finite fields Coding theory