On some algorithms on the proposed lower bound of the designed minimum distance for cyclic codes

The minimum distance for linear codes is one of the important parameters. The shift bound is a good lower bound of the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa codes. It is necessary to construct the maximum number of the independent set for the calculation of the shift bound. However, its computational complexity is very large, because the construction of the independent sets is not unique. The authors proposed an algorithm for calculation of the independent set and new lower bound using the discrete Fourier transform in 2010. In this paper we give simple modification and new recurrent algorithms to improve the original algorithm.