This thesis is an extension and generalization of the work done by Zhang Pengwei, Li Yong, Chang Hsin-Chiu, Liu Hongqing and Truon Trieu-Kien. In this thesis, a hard decision (HD) scheme is presented to facilitate faster decoding of the quadratic residue codes with a code length less than or equal ??. In the new HD algorithm for any code, the required known syndromes are calculated first, then using the Newton identities for each error cases error-locator polynomials are written. Since for (?,?,?) QR code and (??,?,?) QR code, there are sufficiently consecutive syndromes, so the errorlocator polynomial is directly written. For (??,??,?) QR code and (??,??,?) QR code, for up to two errors there are sufficiently consecutive syndromes, so the error- locator polynomial is directly written, but corrects three errors with new different method. The reliability-based shift-search algorithm can be utilized to decode weight-? error patterns.