Algebraic Geometry Codes from Higher Dimensional Varieties
John B. Little · Series on coding theory and cryptology · 2008
Abstract. This paper is a general survey of work 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. 1.