The most important development in the theory of error-correcting codes in recent 20 years has been the introduction of methods from algebraic geometric curves for the construction of linear codes. These so-called algebraic-geometric codes (AG codes) were introduced by Goppa. In this talk, we present a new construction of linear codes called improved geometric Goppa codes, and also present a method to determine the designed minimum distances for the codes using only linear algebra. These improved geometric Goppa codes are more efficient than the traditional geometric Goppa codes derived from some varieties, which include algebraic curves, hyperplanes, surfaces, and other varieties. For these improved geometric Goppa codes any or less errors can be corrected by the majority voting scheme decoding procedure. As Goppa codes can be used in cryptography, we believe that the improved geometric Goppa codes can also be used in cryptography.

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