Name
Abstract | ||
|---|---|---|
We study self-dual codes over chain rings. We describe a technique for constructing new self-dual codes from existing codes and we prove that for chain rings containing an element c with c² = −1, all self-dual codes can be constructed by this technique. We extend this construction to self-dual codes over principal ideal rings via the Chinese Remainder Theorem. We use torsion codes to describe the structure of self-dual codes over chain rings and to set bounds on their minimum Hamming weight. Interestingly, we find the first examples of MDS self-dual codes of lengths 6 and 8 and near-MDS self-dual codes of length 10 over a certain chain ring which is not a Galois ring. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1504/IJICOT.2010.032133 | IJICoT |
Keywords | Field | DocType |
chinese remainder theorem,principal ideal ring,element c,chain ring,galois ring,near-mds self-dual code,finite commutative chain ring,new self-dual code,mds self-dual code,certain chain ring,self-dual code | Discrete mathematics,Hamming code,Combinatorics,Group code,Chinese remainder theorem,Block code,Expander code,Linear code,Reed–Muller code,Principal ideal,Mathematics | Journal |
Volume | Issue | Citations |
1 | 2 | 9 |
PageRank | References | Authors |
0.73 | 10 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Steven T. Dougherty | 1 | 168 | 38.04 |
| Jon-Lark Kim | 2 | 312 | 34.62 |
| Hongwei Liu | 3 | 46 | 8.23 |