Vivado Design Suite Reed-Solomon Decoder in the description of Reed-Solomon Decoder v9.0 p 20

ERR_CNT Element
The ERR_CNT element gives the number of errors, erasures, and
punctures that were corrected. The width of the element depends on the
input parameters n and k. The width is equal to the number of binary
bits required to represent (n-k). If n-k = 16, for example, the
ERR_CNT element is five bits wide

Could someone explain me the example. 'If n-k = 16, for example, the ERR_CNT element is five bits wide'.
I thought it will be 8=(n-k)/2
EDIT 1: In the example n-k =16, then the number of errors ( error correction capability) is (n-k)/2 or I can compute it as 2*e+E&lt;=(n-k), where e - errors, E- erasures
$\left\lfloor\frac{n-k}2\right\rfloor$ is the maximum number of bit errors that we can guarantee a code can correct for a binary channel.
But that doesn't mean a code can't sometimes correct more! (In general: not all code words have a distance that's equal to the code's minimum distance. It is the case for minimum distance separable codes, like RS codes are, though.)
Then:
RS codes are also used in applications where erasures, not bit flips, happen. You'll find the decoder documentation contains a section on erasure decoding.
You'll also find that a RS code can correct up to $n-k$ erasures – and my guess is that they made the count of that and the count of corrected errors the same width for design consistency reasons, and maybe to make different decoder IP interchangeable.
Note that giving a unsigned number more bits than it needs has no functional or FPGA utilization downside in IP cores: if whatever takes the output uses less bits than it has, the synthesizer will optimize away all calculations resulting in the bits that weren't used.