On Numerical Semigroups and the Order Bound
نویسندگان
چکیده
1 Abstract. Let S ={ s0 = 0 <s1 < ... <si...} ⊆ IN be a numerical non-ordinary semigroup; then set, for each i, νi := # {(si−sj ,sj) ∈ S}. We find a non-negative integer m such that dORD(i)=νi+1 for i ≥ m, where dORD(i) denotes the order bound on the minimum distance of an algebraic geometry code associated to S. In several cases (including the acute ones, that have previously come up in the literature) we show that this integer m is the smallest one with the above property. Furthermore it is shown that every semigroup generated by an arithmetic sequence or generated by three elements is acute. For these semigroups, it is also found the value of m.
منابع مشابه
On some invariants in numerical semigroups and estimations of the order bound
1 Abstract. Let S = {si}i∈IN ⊆ IN be a numerical semigroup. For si ∈ S, let ν(si) denote the number of pairs (si−sj , sj) ∈ S . When S is the Weierstrass semigroup of a family {Ci}i∈IN of one-point algebraicgeometric codes, a good bound for the minimum distance of the code Ci is the Feng and Rao order bound dORD(Ci) := min{ν(sj) : j ≥ i+ 1}. It is well-known that there exists an integer m such ...
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