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Weighted Reed-Muller codes and algebraic-geometric codes

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1 Author(s)
Sorensen, A.B. ; Dept. of Math., Aarhus Univ.

A generalization of the Reed-Muller codes, the weighted Reed-Muller codes, is presented. The code parameters are estimated and the duals are shown also to be weighted Reed-Muller codes. It is shown how the minimum distance of certain algebraic-geometric codes in many cases can be determined exactly or an upper bound can be found, using subcodes which are weighted Reed-Muller codes

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Information Theory, IEEE Transactions on  (Volume:38 ,  Issue: 6 )