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.