The low-frequency polarisation properties of radio sources are poorly studied, particularly in statistical samples. However, the new generation of low-frequency telescopes, such as the Murchison Widefield Array (MWA; the precursor for the low-frequency component of the Square Kilometre Array) offers an opportunity to probe the physics of radio sources at very low radio frequencies. In this paper, we present a catalogue of linearly-polarised sources detected at 216 MHz, using data from the Galactic and Extragalactic All-sky MWA (GLEAM) survey. Our catalogue covers the Declination range $-17^{circ}$ to $-37^{circ}$ and 24 hours in Right Ascension, at a resolution of around 3 arcminutes. We detect 81 sources (including both a known pulsar and new pulsar candidate) with linearly-polarised flux densities in excess of 18 mJy across a survey area of approximately 6400 square degrees, corresponding to a surface density of 1 source per 79 square degrees. The level of Faraday rotation measured for our sources is broadly consistent with those recovered at higher frequencies, with typically more than an order of magnitude improvement in the uncertainty compared to higher-frequency measurements. However, our catalogue is likely incomplete at low Faraday rotation measures, due to our practice of excluding sources in the region where instrumental leakage appears. The majority of sources exhibit significant depolarisation compared to higher frequencies; however, a small sub-sample repolarise at 216 MHz. We also discuss the polarisation properties of four nearby, large-angular-scale radio galaxies, with a particular focus on the giant radio galaxy ESO 422$-$G028, in order to explain the striking differences in polarised morphology between 216 MHz and 1.4 GHz.
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