On the parameters of algebraic-geometry codes related to Arf semigroups

On the parameters of Algebraic Geometry codes related to Arf semigroups

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 results developed to that purpose also provide the dimension of the improved geometric Goppa codes related to these CΩ(P, ρlQ).

On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups

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 second Hamming weight for one point AG codes. In particular, we can obtain the second Feng-Rao distance for the codes defined by asymptotically good towers of function fields whose Weierstrass semi...

On the Graphs Related to Green Relations of Finite Semigroups

In this paper we develop an analog of the notion of the con- jugacy graph of  nite groups for the  nite semigroups by considering the Green relations of a  nite semigroup. More precisely, by de ning the new graphs $Gamma_{L}(S)$, $Gamma_{H}(S)$, $Gamma_{J}(S)$ and $Gamma_{D}(S)$ (we name them the Green graphs) related to the Green relations L R J H and D of a  nite semigroup S , we  first atte...

On representations of algebraic-geometry codes

We show that all algebraic-geometric codes possess a succinct representation that allows for the list decoding algorithms of 9, 6] to run in polynomial time. We do this by presenting a root-nding algorithm for univariate polynomials over function elds when their coeecients lie in nite-dimensional linear spaces, and proving that there is a polynomial size representation given which the root ndin...

Algebraic Geometry Codes