2011/08/31 by Olav Geil, Geil, Olav, Casper Thomsen +1 · 1 citation
Computer Science · Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1108.6185
29 pages, 2 figures, 4 tables
arxiv created 2011/08/31 · arxiv updated 2011/09/01
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.