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The online magma calculator http://magma.maths.usyd.edu.au/calc/ tells me this LFSR corresponds to a primitive polynomial since $$G(X) = X^{23} + X^ {21} + X^{16} + X^{8} + X^5 + X^2 + 1$$ is primitive. Thus, some phase of the output sequence is given by $$tr(\alpha^t)$$ where $tr:GF(2^{23})\rightarrow GF(2)$ is the trace map and $\alpha \in GF(2^{23})$ ...