On relationship between proposed lower bound and well-known bounds for cyclic codes

There have been useful lower bounds for the minimum distance of a cyclic code, BCH bound, Hartmann-Tzeng bound, Roos bound and Shift bound. The authors proposed a lower bound of minimum distance by discrete Fourier transform (DFT) in 2010. The relationship between BCH bound, Hartmann-Tzeng bound and Roos bound, BCH bound, Hartmann-Tzeng bound and Shift bound are known, respectively. However, it´s unknown the relationship between Roos bound, Shift bound and Proposed bound. In this paper, we discuss this relation with the cyclic codes.