Decoding Reed-Solomon Codes Next: Berlekamp's Iterative Algorithm for Up: Encoding/Decoding Reed Solomon Codes Previous: Systematic Form Encoding Decoding Reed-Solomon Codes Let be the transmitted code vector and be the corresponding received vector. Then is the error pattern added by the channel, where is a symbol from GF . Assume that the received vector has errors in positions . Then . Define , , the error location numbers. Then, compute the 2t syndromes as follows: . Expanding we obtain a sequence of 2t algebraic syndrome equations: The syndrome equations can be translated into a series of linear equations by defining the error-locator polynomial . has as its roots the inverses of the error locators : Assume that errors have occurred, where t is the error correcting capability of the code. Then, we obtain the following matrix equation: Berlekamp's Iterative Algorithm for Finding the Error-Locator Polynomial The Forney Algorithm for Computing the Error Magnitudes Erasure Decoding A. Matache Sun Oct 20 17:42:25 PDT 1996