The random $k$-XORSAT matrix is an $m\times n$ random matrix $\mathbf A$ over $\mathbb F_2$ that represents a random instance of the $k$-XORSAT problem. Each row of $\mathbf A$ contains precisely $k\geq3$ non-zero entries in random positions. The rows are drawn independently. The matrix $\mathbf A$ is known to have full row rank for $m/n$ below the random $k$-XORSAT satisfiability threshold, which is known explicitly [Dubois, Mandler~2002; Pittel, Sorkin~2016]. Motivated by a problem from quantum game theory and refining a result of Cooper, Frieze and Pegden (2019), we determine the limiting distribution of the rank of $\mathbf A$ beyond the satisfiability threshold.

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