Using higher-order Fourier analysis over general fields

@article{Bhattacharyya2015UsingHF,
  title={Using higher-order Fourier analysis over general fields},
  author={Arnab Bhattacharyya and Abhishek Bhowmick},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2015},
  volume={22},
  pages={77}
}
Higher-order Fourier analysis, developed over prime fields, has been recently used in different areas of computer science, including list decoding, algorithmic decomposition and testing. We extend the tools of higher-order Fourier analysis to analyze functions over general fields. Using these new tools, we revisit the results in the above areas. (i) For any fixed finite field K, we show that the list decoding radius of the generalized Reed Muller code over K equals the minimum distance of the… CONTINUE READING
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