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Prikl. Diskr. Mat. Suppl., 2019, Issue 12, Pages 198–202 (Mi pdma471)  

Mathematical Foundations of Informatics and Programming

On the generic complexity of the decoding problem for linear codes

A. N. Rybalov

Omsk State University

Abstract: Generic-case approach to algorithmic problems was introduced by Miasnikov, Kapovich, Schupp and Shpilrain in 2003. This approach studies behavior of an algorithm on typical (almost all) inputs and ignores the rest of inputs. Many classical undecidable or hard algorithmic problems become feasible in the generic case. But there are generically hard problems. In this paper, we consider generic complexity of the decoding problem for linear codes over finite fields. We fit this problem in the frameworks of generic complexity and prove that its natural subproblem is generically hard provided that this problem is hard in the worst case.

Keywords: generic complexity, linear codes, McEliece cryptosystem.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-41-550001_а


DOI: https://doi.org/10.17223/2226308X/12/56

Full text: PDF file (631 kB)
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UDC: 510.52

Citation: A. N. Rybalov, “On the generic complexity of the decoding problem for linear codes”, Prikl. Diskr. Mat. Suppl., 2019, no. 12, 198–202

Citation in format AMSBIB
\Bibitem{Ryb19}
\by A.~N.~Rybalov
\paper On the generic complexity of the decoding problem for linear codes
\jour Prikl. Diskr. Mat. Suppl.
\yr 2019
\issue 12
\pages 198--202
\mathnet{http://mi.mathnet.ru/pdma471}
\crossref{https://doi.org/10.17223/2226308X/12/56}
\elib{https://elibrary.ru/item.asp?id=41153932}


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