Decoding Quadratic Residue Codes Based on Bivariate Weak-Locator Polynomials

It is well known that quadratic residue codes are an important class of error-correcting codes with large minimum distance and one-half code rate. In this paper, the algebraic decoding of quadratic residue codes is described by using the bivariate weak-locator polynomials, which is a generalization of the univariate weak-locator polynomial. A practical method to generate the bivariate weak-locator polynomials for quadratic residue codes is provided. Experimental results show an example for decoding the quadruple-error-correcting binary quadratic residue code of length 41.