A Viewpoint on the Decoding of the Quadratic Residue Code of Length 89

A viewpoint on the weight-6 error patterns of the algebraic decoding of the (89, 45, 17) quadratic residue (QR) code with reducible generator polynomial, proposed by Truong et al. (2008), is presented in this paper. Some weight-6 error patterns will cause a zero value in the syndrome S1. However, in this case, the inverse-free Berlekamp-Massey (IFBM) algorithm is still valid to determine the error-locator polynomial of six errors in the finite field GF(211). An example demonstrates the fact.