Weighted Reed-Muller codes and algebraic-geometric codes

  • Authors:

  • A. B. Sorensen

  • Affiliations:

  • Dept. of Math., Aarhus Univ.

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

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