Name
Abstract | ||
|---|---|---|
We define the notion of weighted projective Reed–Muller codes over a subset X⊂P(w1,…,ws) of a weighted projective space over a finite field. We focus on the case when X is a projective weighted torus. We show that the vanishing ideal of X is a lattice ideal and relate it with the lattice ideal of a minimal presentation of the semigroup algebra of the numerical semigroup Q=〈w1,…,ws〉⊂N. We compute the index of regularity of the vanishing ideal of X in terms of the weights of the projective space and the Frobenius number of Q. We compute the basic parameters of weighted projective Reed–Muller codes over a 1-dimensional weighted torus and prove they are maximum distance separable codes. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1016/j.ffa.2014.11.009 | Finite Fields and Their Applications |
Keywords | Field | DocType |
primary,secondary | Combinatorics,Finite field,Algebra,Separable space,Torus,Numerical semigroup,Weighted projective space,Semigroup,Quaternionic projective space,Mathematics,Projective space | Journal |
Volume | Issue | ISSN |
33 | C | 1071-5797 |
Citations | PageRank | References |
2 | 0.66 | 15 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Eduardo Dias | 1 | 2 | 0.66 |
| Jorge Neves | 2 | 7 | 1.24 |