An algorithm for new lower bound of minimum distance by DFT for cyclic codes

For cyclic codes some well-known lower bounds and some decoding methods up to the half of the bounds are suggested. Particularly, the shift bound is a good lower bound of the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa codes. However, the computational complexity of the shift bound is very large. In this paper we consider cyclic codes defined by their defining set, and a new method of the minimum distance using the discrete Fourier transform(DFT) is shown. Moreover some examples of binary cyclic codes are given.