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

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1 Author(s)
Staiger, L. ; Dept. of Math., Tech. Univ. of Magdeburg, East Germany

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

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Information Theory, IEEE Transactions on  (Volume:35 ,  Issue: 1 )