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Evaluation codes have been studied since some years ago. At the very beginning they were called projective Reed-Muller type codes and their main parameters (length, dimension and minimum distance) were computed in several particular cases. In fact, the length and dimension of the evaluation codes arising from a complete intersection are known. In this paper… (More)

Let K be a finite field, let X ⊂ P m−1 and X ′ ⊂ P r−1 , with r < m, be two algebraic toric sets parameterized by some monomials in such a way that X ′ is embedded in X. We describe the relations among the main parameters of the corresponding parameter-ized linear codes of order d associated to X and X ′ by using some tools from commutative algebra and… (More)

- Manuel González Sarabia, Joel Nava, Lara, Carlos Rentería Márquez, Eliseo Sarmiento Rosales
- 2013

In this paper we will compute the main parameters of the parameteri-zed codes arising from cycles. In the case of odd cycles the corresponding codes are the evaluation codes associated to the projective torus and the results are well known. In the case of even cycles we will compute the length and the dimension of the corresponding codes and also we will… (More)

In this paper we establish bounds for the main parameters of parameterized codes associated to the edges of a simple graph $$\mathcal {G}$$ G by using the relationships among these parameters and the corresponding ones of the parameterized codes associated to the edges of any subgraph of $$\mathcal {G}$$ G . These inequalities are used to find bounds in the… (More)

In this paper we estimate the main parameters of some evaluation codes which are known as projective parameterized codes. We find the length of these codes and we give a formula for the dimension in terms of the Hilbert function associated to two ideals, one of them being the vanishing ideal of the projective torus. Also we find an upper bound for the… (More)

- Manuel González Sarabia, Eduardo Camps, Eliseo Sarmiento, Rafael H. Villarreal
- ArXiv
- 2016

In this paper we find the second generalized Hamming weight of some evaluation codes arising from a projective torus, and it allows to compute the second generalized Hamming weight of the codes parameterized by the edges of any complete bipartite graph. Also, at the beginning, we obtain some results about the generalized Hamming weights of some evaluation… (More)

In this paper we work with some evaluation codes arising from a specific subset of the projective space. We compute the a−invariant of the corresponding coordinate ring and the main parameters of these codes: length, dimension and minimum distance. We obtain that these codes are MDS codes.

The main goal of this paper is to compare the main parameters of some evaluation codes arising from sets of points in the projective space. A particular example will relate these parameters with the main parameters of some linear codes which are known as Generalized Reed-Solomon codes.