Sudan-decoding generalized geometric Goppa codes

Agnes Eileen Heydtmann

doi:10.1016/S1071-5797(02)00017-5

Sudan-decoding generalized geometric Goppa codes

Agnes Eileen Heydtmann

Research output: Contribution to journal › Journal article › Research › peer-review

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.

Original language	English
Journal	Finite Fields and Their Applications
Volume	9
Issue number	3
Pages (from-to)	267-285
ISSN	1071-5797
DOIs	https://doi.org/10.1016/S1071-5797(02)00017-5
Publication status	Published - 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.",

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AB - 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.

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DO - 10.1016/S1071-5797(02)00017-5

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JO - Finite Fields and Their Applications

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Sudan-decoding generalized geometric Goppa codes

Abstract

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