Abstract. 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 behaviour of such bounds for r ≥ 2 differs from that of the classical Feng-Rao distance (r = 1) by the so-called Feng-Rao numbers. This paper is addressed to compute the Feng-Rao numbers for numerical semigroups of embedding dimension two (with two generators), obtaining a closed simple formula for the general case by using numerical semigroup techniques. These involve the computation of the Apéry set with respect to an integer of the semigroups under consideration. The formula obtained is applied to lower-bounding the generalized Hamming weights, improving the bound given by Kirfel and Pellikaan in terms of the classical Feng-Rao distance. We also compare our bound with a modification of the Griesmer bound, improving this one in many cases.

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 in"nity of a singular plane model for the curve. As a byproduct, the method also provides us with a basis for the spaces L(mP) and the computation of the Feng}Rao distance for the corresponding array of geometric Goppa codes. A general computation of the Feng}Rao distance is also obtained. Everything can be applied to the decoding problem by using the majority scheme of Feng and Rao. Academic Press

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Abstract. 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 th Feng-Rao number is obtained.

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