# The Satisfiability Threshold For Random Linear Equations

Pu Gao
Noëla Müller

Combinatorica, pp. 179-235, 2020.

Keywords:
05C80 05C50

Abstract:

Let A be a random m × n matrix over the finite field $\mathbb{F}_q$ with precisely k non-zero entries per row and let $y\in\mathbb{F}_q^m$ be a random vector chosen independently of A. We identify the threshold m/n up to which the linear system Ax = y has a solution with high probability and analyse the geometry of the set of solution...More

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