Weighted Reed-Muller codes revisited

نویسندگان

  • Olav Geil
  • Casper Thomsen
چکیده

We consider weighted Reed-Muller codes over point ensemble S1 × · · · × Sm where Si needs not be of the same size as Sj . For m = 2 we determine optimal weights and analyze in detail what is the impact of the ratio |S1|/|S2| 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.

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عنوان ژورنال:
  • Des. Codes Cryptography

دوره 66  شماره 

صفحات  -

تاریخ انتشار 2013