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We present the Arcminute Microkelvin Imager (AMI) Large Array catalogue of139 gamma-ray bursts (GRBs). AMI observes at a central frequency of 15.7 GHzand is equipped with a fully automated rapid-response mode, which enables thetelescope to respond to high-energy transients detected by Swift. On receivinga transient alert, AMI can be on-target within two minutes, scheduling laterstart times if the source is below the horizon. Further AMI observations aremanually scheduled for several days following the trigger. The AMI GRBprogramme probes the early-time (< 1 day) radio properties of GRBs, and hasobtained some of the earliest radio detections (GRB 130427A at 0.36 and GRB130907A at 0.51 days post-burst). As all Swift GRBs visible to AMI areobserved, this catalogue provides the first representative sample of GRB radioproperties, unbiased by multi-wavelength selection criteria. We report thedetection of six GRB radio afterglows that were not previously detected byother radio telescopes, increasing the rate of radio detections by 50% over an18-month period. The AMI catalogue implies a Swift GRB radio detection rate of>15%, down to ~0.2 mJy/beam. However, scaling this by the fraction of GRBs AMIwould have detected in the Chandra & Frail sample (all radio-observed GRBsbetween 1997 - 2011), it is possible ~44 - 56% of Swift GRBs are radio-bright,down to ~0.1 - 0.15 mJy/beam. This increase from the Chandra & Frail rate(~30%) is likely due to the AMI rapid-response mode, which allows observationsto begin while the reverse-shock is contributing to the radio afterglow.

The Arcminute Microkelvin Imager Catalogue of Gamma-ray Burst afterglows at 15.7 GHz