A new effective decoding algorithm is presented for arbitrary algebraicgeometric codes on the basis of solving a generalized key equation with the majority coset scheme of Duursma. It is an… (More)

In this paper we compute the order (or Feng-Rao) bound on the minimum distance of one-point algebraic geometry codes CΩ(P, ρlQ), when the Weierstrass semigroup at the point Q is an Arf semigroup. The… (More)

In this paper, we consider some practical applications of the symbolic Hamburger-Noether expressions for plane curves, which are introduced as a symbolic version of the so-called Hamburger-Noether… (More)

We present an algorithm to compute the Weierstrass semigroup at a point P together with functions for each value in the semigroup, provided P is the only branch at infinity of a singular plane model… (More)

The weight hierarchy of one-point algebraic geometry codes can be estimated by means of the generalized order bounds, which are described in terms of a certain Weierstrass semigroup. The asymptotical… (More)

We give some general results concerning the computation of the generalized Feng-Rao numbers of numerical semigroups. In the case of a numerical semigroup generated by an interval, a formula for the r… (More)

We describe the second (generalized) Feng-Rao distance for elements in an Arf numerical semigroup that are greater than or equal to the conductor of the semigroup. This provides a lower bound for the… (More)

We use the study of bilinear forms over a finite field to give a decomposition of the linear codes similar to the one in [10] for generalized toric codes. Such decomposition, called geometric… (More)