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The $k$-XORSAT threshold revisited (2301.09287v1)
Published 23 Jan 2023 in math.CO and cs.DM
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, M\"uller: Combinatorica 2020]. The proof combines physics-inspired message passing arguments with a surgical moment computation.