Title: On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups,
Abstract: 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 semigroups are inductive. In addition, we compute the second
Feng-Rao number, and provide some examples and comparisons with previous
results on this topic. These calculations rely on Apéry sets, and thus
several results concerning Apéry sets of Arf semigroups are presented.