Unlike older cars, there is no compressor speed signal. Thus, a belt slip will not directly disable the compressor, for example when the belt gets wet. However, if the compressor locks up, the belt will slip very badly and will blow the (non-replaceable) thermal fuse in the clutch.

Search for the procedure to extract the codes. The last step is to clear them. If you didn't clear any codes yet, don't suspect anything else until you do. Be sure to write them down.