Optimal covering polynomial sets and soft-decision error-trapping decoding

The covering polynomial method is an effective and simple way to decode cyclic codes. Essentially the idea is to augment an error-trapping decoder by adding a small search through error patterns in the information positions. Although it works best with codes having relatively small rate and correcting a small number of errors, it can be effectively extended to other cases with proper choices of the covering polynomial sets. Our goal is to find the minimal set of covering polynomials that traps all error patterns of given weight τ for given (n,k) cyclic code