Algebraic geometry codes from higher dimensional varieties

2008/02/16 by John B. Little, Little, John B.
Computer Science · Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT

paper · pdf · doi:10.48550/arxiv.0802.2349

26 pages

arxiv created 2008/02/16 · arxiv updated 2009/12/01

Abstract

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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