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

Let S = {si}iIN IN be a numerical semigroup. For si S, let (si) denote the number of pairs (si -sj, sj) S2 . When S is the Weierstrass semigroup of a family {Ci}iIN 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). It is well-known that there exists an integer m such that dORD(Ci) = (si+1) for each i m. By way of some suitable parameters related to the semigroup S, we find upper bounds for m and we evaluate m exactly in many cases. Further we conjecture a lower bound for m and we prove it in several classes of semigroups. Index Therms. Numerical semigroup, Weierstrass semigroup, AG code, order bound on the minimum distance, Cohen-Macaulay type.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Anna Oneto, Grazia Tamone
• Keywords: CORR 2010, Education, Numerical Semigroup, Semigroup, Weierstrass Semigroup