Goppa-like bounds for the generalized Feng-Rao distances. (Q1811099)

This paper presents some general bounds and formulas for the generalized Feng-Rao distances in an arbitrary numerical semigroup. The results obtained in the paper generalize the known results on the classical Feng-Rao distance, particularly its connection with the Goppa distance. These results show that their asymptotical behaviour is essentially the same as in the case of the classical order bound. Using the theory of Apéry generators and relations, explicit computations are also given for the second Feng-Rao distance.