Every transfer of information is subject to some probability of error. Codingtheory addresses the problems of detecting and correcting the errors which occurin these transmissions. Claude E. Shannon's 1948 paper, A mathematical theoryof communications [15], provided theoretical limits of efficiency for codes acrossa given channel, motivating the search for codes as close to these limits as pos-sible. Algebraic geometric codes were introduced by V. D. Goppa in [3] as codeswith very good parameters with respect to Shannon's theory, however it waslater discovered that every linear code may be obtained using a generalizationof Goppa's method. This thesis will describe the construction of algebraic geo-metric codes and discuss a clever efficient method of decoding by T. Johnsen D.Coles and T. Bouganis based on the geometry of the curves used to construct thecodes.INDEXWORDS:Coding Theory, Algebraic Geometry, Algebraic Codes
