SETH-Hardness of Coding Problems
Author(s)Stephens-Davidowitz, Noah; Vaikuntanathan, Vinod
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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.
2019 IEEE 60th Annual Symposium on Foundations of Computer Science
Institute of Electrical and Electronics Engineers (IEEE)
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
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