Arf semigroup and applications to algebraic curves

An important part of the work on numerical semigroups are based on theory of algebraic curves. Numerical semigroups are important because of applications to coding theory and algebraic curves. In this thesis, firstly we give general properties of a numerical semigroups.Numerical semigroups of some curve classes at a Weierstrass points Q are investigated and checked whether these are Arf numerical semigroup or not. Moreover, we compute the Feng-Rao (order bound) bound on the minimum distance of one point-algebraic geometric codes, when the numerical semigroup at the point Q is an Arf semigroup, via Bras-Amoros (2000,2005,2007), Campillo at all (2004). It has been observed that one can construct algebraic geometric codes with better parameters. We believe that Arf numerical semigroups may suggest new tecniques for the codes with better parameters. KEYWORDS:Arf semigroup, Feng-Rao (order bound), one-point codes