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On some invariants in numerical semigroups and estimations of the order bound (1002.1744v1)
Published 9 Feb 2010 in cs.IT, cs.DM, math.AC, and math.IT
Abstract: We study suitable parameters and relations in a numerical semigroup S. When S is the Weierstrass semigroup at a rational point P of a projective curve C, we evaluate the Feng-Rao order bound of the associated family of Goppa codes. Further we conjecture that the order bound is always greater than a fixed value easily deduced from the parameters of the semigroup: we also prove this inequality in several cases.