On the weight distribution of linear codes having dual distance d'>or=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'>or=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.<
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