A complete characterization of pulse shape and phase of a 1.3 microm, monolithic-two-section, quantum-dot mode-locked laser (QD-MLL) at a repetition rate of 40 GHz is presented, based on frequency resolved optical gating. We show that the pulse broadening of the QD-MLL is caused by linear chirp for all values of current and voltage investigated here. The chirp increases with the current at the gain section, whereas larger bias at the absorber section leads to less chirp and therefore to shorter pulses. Pulse broadening is observed at very high bias, likely due to the quantum confined stark effect. Passive- and hybrid-QD-MLL pulses are directly compared. Improved pulse intensity profiles are found for hybrid mode locking. Via linear chirp compensation pulse widths down to 700 fs can be achieved independent of current and bias, resulting in a significantly increased overall mode-locking range of 101 MHz. The suitability of QD-MLL chirp compensated pulse combs for optical communication up to 160 Gbit/s using optical-time-division multiplexing are demonstrated by eye diagrams and autocorrelation measurements.