Patent ID: 8078943

Claim:
An error correction system comprising: an encoder operable to generate an encoded codeword of a polynomial code over a Galois field GF(q) comprising q elements, the encoded codeword comprising a plurality of symbols wherein each symbol comprises one of the q elements, the encoder operable to: add at least one check symbol to an input data sequence d n . . . d 2 , d 1 , d 0 to generate a data polynomial; and append redundancy symbols to the data polynomial to form the encoded codeword, wherein the encoded codeword is transmitted through a channel; and a decoder for decoding a received codeword received from the channel into the encoded codeword, the decoder operable to: correct at least one error in the received codeword to generate a corrected codeword; evaluate at least one symbol of the corrected codeword relative to the check symbol in order to detect a shift error; and when the shift error is detected, shift the corrected codeword to correct the shift error.