Reproduce “Combinatorial limitations of list-decoding Reed-Solomon codes” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Omar Alrabiah, Rohan Goyal, Venkatesan Guruswami
The authors construct full-length Reed–Solomon codes with large lists by making one received word and many valid messages share agreements while retaining common high-degree structure. Over extension fields, they obtain lists of size at least n^{Ω_q(log n)} at two rates near the Johnson radius; over prime fields, infinitely many codes have at least n nearby codewords, refuting constant-list bounds below capacity.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.