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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.
Citation:
A. N. Rybalov, “On the generic complexity of the decoding problem for linear codes”, Prikl. Diskr. Mat. Suppl., 2019, no. 12, 198–202
Linking options:
https://www.mathnet.ru/eng/pdma471 https://www.mathnet.ru/eng/pdma/y2019/i12/p198
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Abstract page: | 127 | Full-text PDF : | 32 | References: | 17 |
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