(I was bored earlier this morning).
I decided to see for a particular 4 bytes id from a dvd sector, how many different 2 bytes for the id error check bytes would give back a zero syndrome. Basically looking for the possibility of false positives. (In principle, there shouldn’t be any false positives).
So I wrote some code which did this as a brute force search of going through all possible 2 bytes for the id error check bytes, and finding which particular 2 byte sets give back a zero syndrome with a particular 4 bytes id. I ran this code for the first several hundred sectors lbas on a particular dvd disc.
Lo and behold (but not too surprising) for each particular 4 bytes id, a brute force search found one corresponding set of 2 bytes which gave back a zero syndrome. Comparing with previous results from actual dvds, they were a respective match for the first several hundred sectors I looked at.
I wouldn’t be surprised if back in the early-1990s when the dvd spec was first being proposed, some company like Toshiba, Sony, etc … actually gave an engineering/tech intern this actual brute force calculation to do as a small project. Basically to explicitly show that there’s no false positives for the particular range of sector ids which dvd would be using.