This random number table doesn't look anything special - it's just all numbers from 0 to 255 randomly shuffled. The kind of thing you could quite trivially create yourself, in other words, and there's no reason to copy from Doom.

Reverse the list and read it bottom to top. ?

Also, I found this.

For a work to be eligible for protection under U.S. copyright law, it must be the product of a minimal amount of creativity. What does that mean for straight collections of facts, such as might be found in lists, personal directories, and other sorts of databases?

If no creativity was employed in selecting or arranging the data, the compilation will not receive copyright protection.

And this for anyone interested in Doom's RNG. It's a cool video for any game programmer/designer.

21st Century Moose said:

This random number table doesn't look anything special - it's just all numbers from 0 to 255 randomly shuffled. The kind of thing you could quite trivially create yourself, in other words, and there's no reason to copy from Doom.

It would make sense to copy Doom's random numbers for compatibility reasons (i.e. a source port that aims for very strict emulation), but in any other case you are only “copying” the general algorithm of using a lookup table containing a random permutation and generating your own random permutation is a simpler and higher quality option than copying one (maybe incorrectly).