Improvements On Goppa Bounds Of One-point AG Codes From Algebraic Curves

The connection between algebraic geometry and coding theory wasdiscovered by V.D.Goppa who constructed linear error correcting codes onalgebraic curves,so the algebraic geometry code was got a lot of attentionin the field of the coding theory.With the development of algebraicgeometric codes,some special codes of algebraic geometric codes were gotmore research,especially for Hermitian codes whose properties were fullyresearched.We want to get a code with better parameters in order to ensurethe higher transmission efficiency,such as short code length and largerminimum distance.Under the same condition in the code length anddimension,we choose the special divisor to improve the Goppa bound in thispaper.This paper consists of three chapters,and it is organized as follow:In the first chapter,we give a brief introduction of algebraic geometrycodes and the main conclusion of this paper.In the second chapter,we givesome basic concepts and theorems about algebraic function fields andalgebraic geometry codes.In the last chapter,we proof the existence of aspecial divisor to improve the Goppa bounds,and give some examples in theend.