Ultrashort pulse propagation through grating-assisted codirectional couplers (GACCs) operating in the linear regime is theoretically investigated. For this purpose, the temporal responses of uniform GACCs to ultrashort optical pulses are calculated and the effects of varying the different physical grating parameters (e.g., length and coupling strength) on these temporal responses are evaluated. We will show that the most interesting pulse reshaping operations occur typically for the "energy receptor" mode and that depending on the length and coupling strength of the uniform perturbation one can achieve very different temporal shapes at the output of the device, including triangular pulses, square temporal waveforms as well as sequences of equalized multiple pulses. Moreover, the temporal scales of the pulses generated from a GACC are generally much shorter (in more than one order of magnitude) than those that can be generated from an equivalent Bragg grating (with the same grating length).