Name
Abstract | ||
|---|---|---|
In 1988 Lachaud introduced the class of projective Reed–Muller codes, defined by evaluating the space of homogeneous polynomials of a fixed degree d on the points of \(\mathbb {P}^n(\mathbb {F}_q)\). In this paper we evaluate the same space of polynomials on the points of a higher dimensional scroll, defined from a set of rational normal curves contained in complementary linear subspaces of a projective space. We determine a formula for the dimension of the codes, and the exact value of the dimension and the minimum distance in some special cases. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/s10623-018-00603-8 | Designs, Codes and Cryptography |
Keywords | Field | DocType |
Projective variety codes,Evaluation codes,Reed–Muller type codes,Higher dimensional scroll,11T71,13P25,94B60 | Scroll,Combinatorics,Polynomial,Homogeneous,Linear subspace,Mathematics,Projective space,Projective test | Journal |
Volume | Issue | ISSN |
87 | 9 | 1573-7586 |
Citations | PageRank | References |
0 | 0.34 | 6 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Cícero Carvalho | 1 | 48 | 7.81 |
| Xavier Ramírez-Mondragón | 2 | 0 | 0.34 |
| Victor G. L. Neumann | 3 | 6 | 2.68 |
| Horacio Tapia-Recillas | 4 | 32 | 6.12 |