Sudan-decoding generalized geometric Goppa codes

Authors:
Agnes E. Heydtmann
Affiliations:
Department of Mathematics, Technical University of Denmark, Building 303, Matematiktorvet, DK-2800 Kongens Lyngby, Denmark
Venue:
Finite Fields and Their Applications
Year:
2003

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Abstract

Generalized geometric Goppa codes are vector spaces of n-tuples with entries from different extension fields of a ground field. They are derived from evaluating functions similar to conventional geometric Goppa codes, but allowing evaluation in places of arbitrary degree. A decoding scheme for these codes based on Sudan's improved algorithm is presented and its error-correcting capacity is analyzed. For the implementation of the algorithm it is necessary that the so-called increasing zero bases of certain spaces of functions are available. A method to obtain such bases is developed.