The $k$-XORSAT Threshold Revisited

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...

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Bibliographic Details
Published inThe Electronic journal of combinatorics Vol. 31; no. 2
Main Authors Coja-Oghlan, Amin, Kang, Mihyun, Krieg, Lena, Rolvien, Maurice
Format Journal Article
LanguageEnglish
Published 19.04.2024
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Summary: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.
ISSN:1077-8926
1077-8926
DOI:10.37236/11815