Construct an LFSR that will go through 2³⁰ 1 distinct states before it loops. You can specify the LFSR as either a diagram or a recurrence relation.

Output the first 500 output bits of the LFSR if it starts in the initial state (1, 0, 0, . . . , 0, 0, 0, 1). Please provide your output in the format of a text file of zeros and ones, with no spaces, commas, or other delimiters in between.

For example for the first 10 bits of a degree 4 LFSR producing a cycle of 15 states and starting from the state (1, 0, 0, 1) would be "1001101011"