Name
Abstract | ||
|---|---|---|
We construct an infinite family of two-Lee-weight and three-Lee-weight codes over the non-chain ring Fp+uFp+vFp+uvFp, where u2=0,v2=0,uv=vu. These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. With a linear Gray map, we obtain a class of abelian three-weight codes and two-weight codes over Fp. In particular, the two-weight codes we describe are shown to be optimal by application of the Griesmer bound. We also discuss their dual Lee distance. Finally, an application to secret sharing schemes is given. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.disc.2017.09.003 | Discrete Mathematics |
Keywords | Field | DocType |
Weight distribution,Gauss sum,Griesmer bound,Secret sharing schemes | Discrete mathematics,Abelian group,Lee distance,Combinatorics,Secret sharing,Gauss sum,Algebraic structure,Expander code,Linear code,Weight distribution,Mathematics | Journal |
Volume | Issue | ISSN |
341 | 2 | 0012-365X |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yan Liu | 1 | 5 | 2.53 |
| Minjia Shi | 2 | 18 | 4.00 |
| Patrick Solé | 3 | 45 | 12.57 |