This paper derives six different forms of message length functions for the general linear regression model. In so doing, two different prior densities and the idea of parameter orthogonality are employed. Parameter estimates are then obtained by finding those parameter values which minimize the message length. The asymptotic properties of the minimum message length (MML) estimators are studied and it is shown that these estimators are asymptotically normal. A Monte Carlo experiment was conducted to investigate the small sample properties of the MML estimators in the context of first-order moving average regression disturbances. The results show that the combination of parameter orthogonality and message length based inference can produce good small sample properties.