Local list-decoding and testing of random linear codes from high-error

@article{Kopparty2009LocalLA,
  title={Local list-decoding and testing of random linear codes from high-error},
  author={Swastik Kopparty and Shubhangi Saraf},
  journal={SIAM J. Comput.},
  year={2009},
  volume={42},
  pages={1302-1326}
}
In this paper, we give surprisingly efficient algorithms for list-decoding and testing random linear codes. Our main result is that random sparse linear codes are locally list-decodable and locally testable in the high-error regime with only a constant number of queries. More precisely, we show that for all constants c> 0 and γ > 0, and for every linear code C ⊆ 0,1N which is: sparse: |C| ≤ Nc, and unbiased: each nonzero codeword in C has weight in (1/2 - N-γ, 1/2 + N-γ), C is locally testable… CONTINUE READING
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