Author:
Coja-Oghlan Amin,Kang Mihyun,Krieg Lena,Rolvien Maurice
Abstract
We provide a simplified proof of the random $k$-XORSAT satisfiability threshold theorem. As an extension we also determine the full rank threshold for sparse random matrices over finite fields with precisely $k$ non-zero entries per row. This complements a result from [Ayre, Coja-Oghlan, Gao, Müller, Combinatorica, 2020]. The proof combines physics-inspired message passing arguments with a surgical moment computation.
Publisher
The Electronic Journal of Combinatorics