The primary objectives of this research are to find decoding algorithms for the Quadratic Residue (QR) Codes, including the well known (23,12,7) Golay code, the (31,16,7) QR code and the (41,21,9) code. The key idea is to find the error locator polynomial by a systematic use of the Newton identities associated with the code syndromes. The study focusses on the binary QR codes which have length 8m+/- 1. The techniques developed extend the algebraic decoding algorithm found recently by the PI for the (31,16,7) QR code and by Elia for the (23,12,7) Golay code to more general QR codes. The first new example of this extension is the (41,21,9) QR code. Is expected that this work and the algebraic methods developed here can apply generally to the entire set of QR codes and to other codes such as the BCH and Reed-Solomon codes.
