Subfield-Subcodes of Generalized Toric codes

Details Subfield-Subcodes of Generalized Toric codes Subfield-Subcodes of Generalized Toric codes

2010-05-11

arxiv.org/abs/1005.1871v1

Computer Science

Information Theory

Submitted to 2010 IEEE International Symposium on Information Theory (ISIT 2010)

Scientific paper

We study subfield-subcodes of Generalized Toric (GT) codes over $\mathbb{F}_{p^s}$. 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.

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