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Qualifying Exam
3/5/2018 10:00 am
CoRE B (305)

Syndrome decoding of Reed-Muller codes and tensor decomposition over finite fields

Aditya Potukuchi, Dept. of Computer Science

Examination Committee: Prof. Swastik Kopparty (Chair), Prof. Shubhangi Saraf, Prof. Jeff Kahn, Prof. Yongfeng Zhang


In this talk, we will look at decoding Reed-Muller codes beyond their minimum distance when the errors are random (i.e., in the binary symmetric channel). A recent beautiful result of Saptharishi, Shpilka and Volk showed that for binary Reed-Muller codes of length n and degree n - O(1), one can correct polylog(n) random errors in poly(n) time (which is well beyond the worst-case error tolerance of O(1)). We will see two efficient algorithms as well as a different proof of the same result, where the decoding is done given the polylog(n)-bit long syndrome vector of the corrupted codeword: