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### Partial feedback linearization (Control theory)

Greetings,
I'm trying to understand a theorem about partial feedback linearization from a paper "On the largest feedback linearizable subsystem" by R.Marino (you can find it here: ...

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### How are taps proven to work for LFSRs?

Obviously you can exhaustively check that it lands on every state except the zero state, but for large LFSRs, this quickly becomes infeasible.
Wikipedia states the following on its LFSR page:
The ...