Name
Abstract | ||
|---|---|---|
The purpose of this paper is to study codes over finite principal ideal rings. To do this, we begin with codes over finite chain rings as a natural generalization of codes over Galois rings GR(p e , l) (including $${\mathbb{Z}_{p^e}}$$ ). We give sufficient conditions on the existence of MDS codes over finite chain rings and on the existence of self-dual codes over finite chain rings. We also construct MDS self-dual codes over Galois rings GF(2 e , l) of length n = 2 l for any a 驴 1 and l 驴 2. Torsion codes over residue fields of finite chain rings are introduced, and some of their properties are derived. Finally, we describe MDS codes and self-dual codes over finite principal ideal rings by examining codes over their component chain rings, via a generalized Chinese remainder theorem. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/s10623-008-9215-5 | Des. Codes Cryptography |
Keywords | Field | DocType |
Chain ring,Galois ring,MDS code,Principal ideal ring,94B05 | Discrete mathematics,Artinian ring,Combinatorics,Torsion (mechanics),Chinese remainder theorem,Commutative algebra,Noncommutative ring,Von Neumann regular ring,Principal ideal,Mathematics,Principal ideal ring | Journal |
Volume | Issue | ISSN |
50 | 1 | 0925-1022 |
Citations | PageRank | References |
12 | 1.41 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Steven T. Dougherty | 1 | 168 | 38.04 |
| Jon-Lark Kim | 2 | 312 | 34.62 |
| Hamid Kulosman | 3 | 26 | 2.27 |