Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) error correcting codes are widely used in digital technology. An important problem in the implementation of RS and BCH decoding is the fast finding of the error p...Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) error correcting codes are widely used in digital technology. An important problem in the implementation of RS and BCH decoding is the fast finding of the error positions (the roots of error locator polynomials). Several fast root-finding algorithms for polynomials over finite fields have been proposed. In this paper we give a generalization of the Goertzel algorithm. Our algorithm is suitable for the parallel hardware implementation and the time of multiplications used is restricted by a constant.展开更多
基金This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 60433050, 90607005)
文摘Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) error correcting codes are widely used in digital technology. An important problem in the implementation of RS and BCH decoding is the fast finding of the error positions (the roots of error locator polynomials). Several fast root-finding algorithms for polynomials over finite fields have been proposed. In this paper we give a generalization of the Goertzel algorithm. Our algorithm is suitable for the parallel hardware implementation and the time of multiplications used is restricted by a constant.
