New efficient decoding algorithm of the (17, 9, 5) quadratic residue code

Abstract

In recent years, the decoding of quadratic residue (QR) codes has attracted a wide attention, considering their good properties in terms of minimal distance and special mathematic structure that make them one of the most known subclasses of codes in the family of cyclic codes. These codes are known for their complicated decoding procedure and the difficult hardware implementation. In this paper, we propose a new decoding method to decode the (17,9,5) quadratic residue code. This method does require neither the computation of the unknown syndromes nor the error-locator polynomial, instead, it decodes the discussed code by using a simple way to locate the position of the errors. To ensure the validity of the proposed method, we tested all the possible error patterns. and the results were very satisfying since the proposed decoder corrected all of them. So, we declare that this decoder can surely decode up to the to correcting capacity of this code.