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arXiv · 1005.1871

Subfield-Subcodes of Generalized Toric codes

Fernando Hernando·Michael E. O'Sullivan·Emanuel Popovici·Shraddha Srivastava
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Abstract

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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Fernando Hernando, Michael E. O'Sullivan, Emanuel Popovici, Shraddha Srivastava. 2010-05-11. Subfield-Subcodes of Generalized Toric codes. https://doi.org/10.1109/isit.2010.5513688

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