We compare predicted Type Ib/c supernova (SNIb/c) rates with the observed long-duration Gamma-Ray-Burst (GRB) rates both locally and as a function of redshift, by assuming different star formation histories in galaxies of different morphological types. Due to the high star formation in spheroids at high redshift, we predict a large number of GRBs beyond z > 7. Moreover, based on our studies and on the current LAT performance, an estimate of the detection possibility of this burst population is presented.