The Second Feng-Rao Number for Codes Coming From Inductive Semigroups

The second Feng-Rao number of every inductive numerical semigroup is explicitly computed. This number determines the asymptotical behavior of the order bound for the second Hamming weight of one-point algebraic geometry codes. In particular, this result is applied for the codes defined by asymptotically good towers of function fields whose Weierstrass semigroups are inductive. In addition, some properties of inductive numerical semigroups are studied, the involved Apery sets are computed in a recursive way, and some tests to check whether given numerical semigroups are inductive or not are provided.