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We consider a decoding method for cyclic codes up to the Hartmann-Tzeng bound using the discrete Fourier transform. Indeed we propose how to make a submatrix of the circulant matrix from an error vector for this decoding method. Moreover an example of a binary cyclic code, which could not be corrected by BCH decoding but be correctable by proposed decoding, is given. It is expected that this decoding method induces universal understanding for decoding method up to the Roos bound and the shift bound.