No the labels where all pre-printed and just unique, we could not do a seperate server based system to support multiple test fixtures at the time and CEMs can (nearly) always control bar codes to be unique. They can also easily record and match stuff in a database. The labels started with the fixed 3 digit customer code. The programmer read the label and wrote a calculated code to the memory.
No they were set/provided by another person. I just chose to use it in the bar code to help ensure the factory didn't mix up labels or boards in the process.
I couldn't say for sure, but I tend to assume most scanners can do this. I've done it with an embedded scanner and a hand scanner (both > I also used bearer bars top and bottom to help reduce bad reads further.
You cannot eliminate the problem completely , but the using a fixed number of digits and some fixed digits you can dramatically reduce the probability. Although I have to say I've never tried to calculate it.
-- Tony