In the context of coding theory, cyclic codes are an important class of error-correcting codes. These codes have an excellent algebraic structure for error detection and correction and are widely used in data storage systems. Cyclic codes include the Hamming code, Golay code, Bose Chaudhuri-Hocquenghem (BCH) codes, Reed-Solomon (RS) codes and quadratic residue (QR) codes. In the decoding of these codes we have the notion of error-locator and weak-locator polynomials. A class of cyclic codes has recently been decoded by using the weak-locator polynomials instead of the conventional error-locator polynomials. In this research, an appropriate matrix for decoding cyclic codes is introduced which is denoted by SXYW(I; J??), where the determinant of SXYW(I; J??) is zero and is expressed as a bivariate weak-locator polynomial.
