Using rank two vector bundles for fast decoding of Goppa codes
Brown, Angela K.
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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 , 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  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