Subfield-Subcodes of Generalized Toric codes

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

doi:10.1109/ISIT.2010.5513688

Subfield-Subcodes of Generalized Toric codes

Information Theory 2024-05-01 v1 math.IT

Authors: 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.

Keywords

maximum distance separable code coding theory

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@article{arxiv.1005.1871,
  title  = {Subfield-Subcodes of Generalized Toric codes},
  author = {Fernando Hernando and Michael E. O'Sullivan and Emanuel Popovici and Shraddha Srivastava},
  journal= {arXiv preprint arXiv:1005.1871},
  year   = {2024}
}

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

Subfield-Subcodes of Generalized Toric codes

Abstract

Keywords

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