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[Cryptography] Linerar Feeback shift register in Solinas paper



The Solina's paper Generalized Mersenne Numbers [0] contains a Linear Feedback shift register I am not able to understand.
You can find the lfsr i am talking about at page 4 of the paper [0] or simply in this question I made in  the crypto stackexchange site.

It is supposed to be a normal Linear Feedback shift register but it doesn't seem to follow the "normal" lfsr rule. Is anyone able to explain the logic it follows? 

Thanks in advance

antonio

[0] http://cacr.uwaterloo.ca/techreports/1999/corr99-39.pdf
[1] https://crypto.stackexchange.com/questions/55270/linerar-feeback-shift-register
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