/sci/ - Science & Math

This is an NxN square matrix with N ones in it. Does it have some sort of name? Can I represent it with an N bit number, or does it have to be N^2? I want to just get a large integer and turn it into one of these matrices with one-to-one correspondence between the int and the matrix, I'm currently thinking just a series of fixed-width numbers, each saying the place of the ones (so pic related would be (00, 03, 02, 06, 07, 05, 01, 04) but all concatenated, and probably in binary with only enough width to contain the largest number. But I'm pretty sure this isn't very bit-efficient.
Google searching just gets me "matrix full of ones" and "identity matrix".