In this series of three lectures delivered at the NATO Advanced Institute in Vlora, Albania, April 28-May 9, 2008, we present new error-correcting algorithms for geometric Goppa codes, based on rank-2 vector bundles over an algebraic curve. We review the construction of moduli spaces of vector bundles and relevant stratifications and give examples for the Klein curve. We propose questions of algebraic geometry that could be answered using coding theory and vice versa.
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