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SETH-hardness of Coding Problems

Noah Stephens-Davidowitz
Noah Stephens-Davidowitz
Vinod Vaikuntanathan
Vinod Vaikuntanathan

2019 IEEE 60TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS 2019), pp. 287.0-301, 2019.

Cited by: 3|Bibtex|Views19|DOI:https://doi.org/10.1109/FOCS.2019.00027
EI
Other Links: academic.microsoft.com|dblp.uni-trier.de
Keywords:
Coding problemsfine-grained hardnessSETHlinear codes

Abstract:

We show that assuming the strong exponential time hypothesis (SETH), there are no non-trivial algorithms for the nearest codeword problem (NCP), the minimum distance problem (MDP), or the nearest codeword problem with preprocessing (NCPP) on linear codes over any finite field. More precisely, we show that there are no NCP, MDP, or NCPP al...More

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