Understanding confusing algorithm notation

I'm having trouble understanding the notation used by a book in describing a prng testing algorithm. Here are some of the snippets in question:

My confusion is: what is the significance of of j? It's not well defined at all. Is it supposed to be the index of the vectors? How does it not start from 0 then?

Continuing on:

I get that the left arrow is assignment. But again the algorithm is referring to j and only referring to j0 and j1. Again, it seems like it would be the indices of j. But then I'm especially confused by the line, "Then for j <- j, j1 - 1 ..., j0 " because it seems like it's referring to deincrementing the index of j, but it's subtracting from j itself and not the subscript.

Any help much appreciated, thanks.