Linear dependence relations of nonrecurrent syndromes in decoding cyclic codes beyond their design distance

In 1994, Feng at. al. gave a procedure for decoding cyclic codes that is bounded by the minimum distance of a code. The significance of their work lies in the fact that conventional decoding procedures based on the classical key equation are design distance-bounded and so do not exploit the full error-correcting capability of a code. A crucial step in Feng's decoding procedure is the computation of unknown syndromes using linear dependence relations. We present some results that may be used to carry out this important task.