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Elusive bug in LFSR implementation

Okay, so I've put together a basic LFSR class as well as a test driver to verify that it was implemented correctly (the driver employs a brute force approach that simply cycles through every possible configuration). After running a few iterations of the test I compared the results with this document. All of the odd-degree LFSR's seem to be working correctly, but for some reason none of the LFSR's that are built from even-degree polynomials produce maximal length sequences (MLS's). On closer inspection, the longest sequences turned out to be exactly **half** of the MLS for that particular degree of polynomial, and a nominal count of them turned out to be precisely the number of MLS's expected for said degree. So I spent the better half of yesterday on this (and now more in the wee hours today), but I just can't figure out where I went wrong. Can anyone provide some insight into this?