Projective Reed–Muller type codes on rational normal scrolls |
| |
Institution: | Faculdade de Matemática, Universidade Federal de Uberlândia, Av. J. N. Ávila 2121, 38.408-902 Uberlândia, MG, Brazil |
| |
Abstract: | In this paper we study an instance of projective Reed–Muller type codes, i.e., codes obtained by the evaluation of homogeneous polynomials of a fixed degree in the points of a projective variety. In our case the variety is an important example of a determinantal variety, namely the projective surface known as rational normal scroll, defined over a finite field, which is the basic underlining algebraic structure of this work. We determine the dimension and a lower bound for the minimum distance of the codes, and in many cases we also find the exact value of the minimum distance. To obtain the results we use some methods from Gröbner bases theory. |
| |
Keywords: | Projective variety codes Evaluation codes Reed–Muller type codes Gröbner bases |
本文献已被 ScienceDirect 等数据库收录! |
|