Special linear systems on compact Riemann surfaces

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One of main themes of the study of compact Riemann surfaces is a classification problem of Riemann surfaces using the existence of meromorphic function on them and conformal invariants. We have studied this theme and the code theory as an application of it. For conformal invariants on Riemann surfaces, we have dealt with and gotten results on the gonality and the smallest degree of Riemann surfaces represented as a projective plane curve. For the coding theory, we study the algebraic geometric coding theory. We have gotten results concerning the Weierstrass n-tuple for suitable linear systems on Riemann surfaces.