A Fourier-Analytic Approach to List-Decoding for Sparse Random Linear Codes
IEICE transactions on information and systems
It is widely known that decoding problems for random linear codes are computationally hard in general. Surprisingly, Kopparty and Saraf proved query-efficient list-decodability of sparse random linear codes by showing a reduction from a decoding problem for sparse random linear codes to that for the Hadamard code with small number of queries even under high error rate  . In this paper, we show a more direct list-decoding algorithm for sparse random linear codes with small number of queries
... number of queries from a Fourier-analytic approach. key words: list-decoding, Fourier analysis Akinori Kawachi is an assistant professor of Department of Mathematical and Computing Sciences, Tokyo Institute of Technology. Received B.E., M.Info., and Ph.D. degrees from Kyoto University in 2000, 2002, and 2004, respectively. His research interests are computational complexity, quantum computing, and foundations of cryptography. Ikko Yamane is a master student of Department of Computer Science, Tokyo Institute of Technology. Received a B.E. degree from Tokyo Institute of Technology in 2013. His research interests are randomized algorithms and machine learning.