  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.
