# 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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