We present a study of the central radio activity of galaxy clusters at high redshift. Using a large sample of galaxy clusters at $0.7<z<1.5$ from the Massive and Distant Clusters of {it WISE} Survey and the Faint Images of the Radio Sky at Twenty-Centimeters $1.4$~GHz catalog, we measure the fraction of clusters containing a radio source within the central $500$~kpc, which we term the cluster radio-active fraction, and the fraction of cluster galaxies within the central $500$~kpc exhibiting radio emission. We find tentative ($2.25sigma$) evidence that the cluster radio-active fraction increases with cluster richness, while the fraction of cluster galaxies that are radio-luminous ($L_{1.4~mathrm{GHz}}geq10^{25}$~W~Hz$^{-1}$) does not correlate with richness at a statistically significant level. Compared to that calculated at $0 < z < 0.6$, the cluster radio-active fraction at $0 < z < 1.5$ increases by a factor of $10$. This fraction is also dependent on the radio luminosity. Clusters at higher redshift are much more likely to host a radio source of luminosity $L_{1.4~mathrm{GHz}}gtrsim10^{26}$~W~Hz$^{-1}$ than are lower redshift clusters. We compare the fraction of radio-luminous cluster galaxies to the fraction measured in a field environment. For $0.7<z<1.5$, we find that both the cluster and field radio-luminous galaxy fraction increases with stellar mass, regardless of environment, though at fixed stellar mass, cluster galaxies are roughly $2$ times more likely to be radio-luminous than field galaxies.
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