1 Department of Mathematical Sciences, The Faculty of Engineering and Science, Aalborg University, VBN2 The Faculty of Engineering and Science, Aalborg University, VBN3 Aalborg University, VBN
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.
Designs, Codes and Cryptography, 2013, Vol 66, Issue 1-3, p. 195-220