Algebraic geometry codes from higher dimensional varieties

Details Algebraic geometry codes from higher dimensional varieties Algebraic geometry codes from higher dimensional varieties

2008-02-16

arxiv.org/abs/0802.2349v1

Computer Science

Information Theory

26 pages

Scientific paper

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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