SETH-Hardness of Coding Problems
Name
TR19-159 (1).pdf
Description
Accepted version
Size
613.59 KB
Format
Adobe PDF
Checksum (MD5)
6f2c5e08ef8d869f788116d5a710263f
Author(s)
Stephens-Davidowitz, Noah
Vaikuntanathan, Vinod
Date Issued
January 2020
Journal
2019 IEEE 60th Annual Symposium on Foundations of Computer Science
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Stephens-Davidowitz, Noah and Vinod Vaikuntanathan. "SETH-Hardness of Coding Problems." 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, November 2019, Baltimore, Maryland, Institute of Electrical and Electronics Engineers, January 2020. © 2019 IEEE
Version
Author's final manuscript
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 algorithms running in time q (1-ϵ)n for any constant ϵ>0 for codes with qn codewords. (In the case of NCPP, we assume non-uniform SETH.) We also show that there are no sub-exponential time algorithms for γ-Approximate versions of these problems for some constant γ > 1, under different versions of the exponential-Time hypothesis.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/focs.2019.00027
