Name
Abstract | ||
|---|---|---|
Let R be a chain ring with four elements. In this paper, we present two new constructions of R-linear codes that contain a subcode associated with a simplex code over the ring R. The simplex codes are defined as the codes generated by a matrix having as columns the homogeneous coordinates of all points in some projective Hjelmslev geometry PHG(R k ). The first construction generalizes a recent result by Kiermaier and Zwanzger to codes of arbitrary dimension. We provide a geometric interpretation of their construction which is then extended to projective Hjelmslev spaces of arbitrary dimension. The second construction exploits the possibility of adding two non-free rows to the generator matrix of a linear code over R associated with a given point set. Though the construction works over both chain rings with four elements, the better codes are obtained for $${R=\mathbb{Z}_4}$$ . |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s10623-012-9649-7 | Des. Codes Cryptography |
Keywords | Field | DocType |
Simplex code,Chain ring,Projective Hjelmslev space,Hjelmslev plane,Hyperoval,Lee weight,R,-linear code,Gray map,94B05,94B27,51C05,51E21,51E26 | Row,Homogeneous coordinates,Discrete mathematics,Generator matrix,Combinatorics,Matrix (mathematics),Simplex codes,Simplex,Linear code,Point set,Mathematics | Journal |
Volume | Issue | ISSN |
66 | 1-3 | 0925-1022 |
Citations | PageRank | References |
0 | 0.34 | 6 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Thomas Honold | 1 | 71 | 14.01 |
| Ivan Landjev | 2 | 28 | 5.17 |