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I know that in order to find the linear complexity of the two sequence beginnings $$(1,-1,0,-1,0,0,0,0,1,0,\dots)\in\mathbb{Z}_3^\mathbb{N}\\ (2,0,-1,-2,0,0,-2,2,-1,-2,\dots)\in\mathbb{Z}_5^\mathbb{N},$$ I have to find LFSRs that generate these sequences. Do these have to be found by trial and error or is there a better way than trying them with brute force?

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