Algebraic geometry codes from higher dimensional varieties

John B. Little

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Algebraic geometry codes from higher dimensional varieties

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arxiv 0802.2349 v1 pith:2X6O7MUE submitted 2008-02-16 cs.IT math.IT

John B. Little This is my paper · ORCID

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This paper is a general survey of literature on Goppa-type codes from higher dimensional algebraic varieties. The construction and several techniques for estimating the minimum distance are described first. Codes from various classes of varieties, including Hermitian hypersurfaces, Grassmannians, flag varieties, ruled surfaces over curves, and Deligne-Lusztig varieties are considered. Connections with the theories of toric codes and order domains are also briefly indicated.

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