On the weight distribution of linear codes having dual distance d´⩾k

Using only the principle of inclusion and exclusion, the author derives a formula for the weight distribution of an [n,k ] code whose dual code has a minimum distance d´⩾k . The result yields a new condition on the weight distributions of a linear code and its dual which is necessary and sufficient for the code to be a maximum distance separable (MDS) code. Moreover, it shows how the weight distribution for linear MDS codes is obtained in an elementary manner