We study subfield-subcodes of Generalized Toric (GT) codes over
Fps​. These are the multidimensional analogues of BCH codes,
which may be seen as subfield-subcodes of generalized Reed-Solomon codes. We
identify polynomial generators for subfield-subcodes of GT codes which allows
us to determine the dimensions and obtain bounds for the minimum distance. We
give several examples of binary and ternary subfield-subcodes of GT codes that
are the best known codes of a given dimension and length.Comment: Submitted to 2010 IEEE International Symposium on Information Theory
(ISIT 2010