Optimal covering polynomial sets correcting three errors for binary cyclic codes
The covering polynomial method is a generalization of error-trapping decoding and is a simple and effective way to decode cyclic codes. For cyclic codes of rate R   0, equal to nrho + 2rootnrho + (1/2) logphi(n/rho) + O(l), where phi = (1 + root5)/2. For all codes correcting up to three errors, the number of covering polynomials is at least nrho + 2rootnrho + O(log n); covering polynomial sets achieving this bound (and thus within O(log n) of the minimum) are presented in closed-form specifications for rates in the range 11/15 less than or equal to R < 3/4.
covering polynomial cyclic codes error-trapping decoding kasami decoding