Title: Syndrome decoding of Reed-Muller codes andtensor decomposition over finite fields
Speaker: Aditya Potukuchi, Rutgers University
Date: Wednesday, November 15, 2017 11:00am-12:00pm
Location: CoRE Bldg, Room 301, Rutgers University, Busch Campus, Piscataway, NJ
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:
1. The first is via. a connection to the well-studied `tensor decomposition problem'.
2. The second via. a reduction to finding all common roots of a space of low degree polynomials, which is also of independent interest.