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Designs, Codes and Cryptography

, Volume 66, Issue 1–3, pp 195–220 | Cite as

Weighted Reed–Muller codes revisited

  • Olav Geil
  • Casper Thomsen
Article

Abstract

We consider weighted Reed–Muller codes over point ensemble S 1 × · · · × S m where S i needs not be of the same size as S j . For m = 2 we determine optimal weights and analyze in detail what is the impact of the ratio |S 1|/|S 2| on the minimum distance. In conclusion the weighted Reed–Muller code construction is much better than its reputation. For a class of affine variety codes that contains the weighted Reed–Muller codes we then present two list decoding algorithms. With a small modification one of these algorithms is able to correct up to 31 errors of the [49,11,28] Joyner code.

Keywords

Affine variety codes List decoding Weighted Reed–Muller codes 

Mathematics Subject Classification

11T71 94B35 12E20 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematical SciencesAalborg UniversityAalborgDenmark

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