Key Prefix KDF with Counter
I think you're encountering the difference between an academic paper and an implementable standard like an RFC or NIST Special Publication.

In an academic setting, details like encodings rarely matter. Using a uint8, uint16, or plain old int results in the same security in this case. So the counter can be encoded however you wish. 

However, unless you foresee a true need to generate enormous outputs, I would use a single byte and ensure that you return an error if the requested output is larger than 255*(hash length). This prevents the user from mis-using your KDF in an application for which it was not designed.