The second Feng–Rao number for codes coming from telescopic semigroups

In this manuscript we show that the second Feng–Rao number of any telescopic numerical semigroup agrees with the multiplicity of the semigroup. To achieve this result we first study the behavior of Apery sets under gluings of numerical semigroups. These results provide a bound for the second Hamming weight of one-point Algebraic Geometry codes, which improves upon other estimates such as the Griesmer Order Bound.