Recovered coronavirus patients are testing positive again. Can you get reinfected?

In South Korea, health officials are trying to solve a mystery: why 163 people who recovered from coronavirus have retested positive, according to the Korea Centers for Disease Control and Prevention (KCDC).

The same has been recorded in China, where some coronavirus patients tested positive after seeming to recover, although there are no official figures.

That raises the question: can you get reinfected with coronavirus?