Abstract
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.
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.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Designs, Codes and Cryptography |
| Vol/bind | 66 |
| Udgave nummer | 1-3 |
| Sider (fra-til) | 195-220 |
| Antal sider | 26 |
| ISSN | 0925-1022 |
| DOI | |
| Status | Udgivet - 2013 |