On some invariants in numerical semigroups and estimations of the order bound

@article{Oneto2010OnSI,
  title={On some invariants in numerical semigroups and estimations of the order bound},
  author={Anna Oneto and Grazia Tamone},
  journal={Semigroup Forum},
  year={2010},
  volume={81},
  pages={483-509}
}
Let S={si}i∈ℕ⊆ℕ be a numerical semigroup. For si∈S, let ν(si) denote the number of pairs (si−sj,sj)∈S2. When S is the Weierstrass semigroup of a family $\{\mathcal{C}_{i}\}_{i\in\mathbb{N}}$ of one-point algebraic-geometric codes, a good bound for the minimum distance of the code $\mathcal{C}_{i}$ is the Feng and Rao order bounddORD(Ci). It is well-known that there exists an integer m such that dORD(Ci)=ν(si+1) for each i≥m. By way of some suitable parameters related to the semigroup S, we find… 
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