In a recent paper, Tsaban and Vishne [4] introduce linear transformation shift registers (TSRs) which generate sequences by an entire word with each iteration. The authors recently [1] proved that over double-struck F sign2, irreducible TSRs occur in pairs. Now the results are generalized and extended for arbitrary finite fields. This aids in the search for irreducible TSRs.

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Series Lecture Notes in Computer Science
Dewar, M. (Michael), & Panario, D. (2004). Mutual irreducibility of certain polynomials. Lecture Notes in Computer Science.