Remainder Decoding of Binary Quadratic Residue Codes Using the Gao’s Algorithm

Abstract

The quadratic residue (QR) codes whose code rates are greater than or equal 1/2 and generally have high error-correcting capacity are widely used in communication for channel coding. In this paper, a new decoding method is proposed for the binary QR codes. The key ideal behind the proposed method is to apply the properties of remainder decoding and the Gao’s algorithm. In the remainder decoding, the main feature of efficient compute syndromes is contained in our decoding method. And the modified Gao’s algorithm is also used in our decoding algorithm. The new algorithm has been verified by a software simulation using C++ language running through possible error patterns. An example of (17, 9, 5) QR code using this decoding algorithm is given.