Abstract
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 \(\mathbb{F}_2\), irreducible TSRs occur in pairs. Now the results are generalized and extended for arbitrary finite fields. This aids in the search for irreducible TSRs.
The first author was supported by an NSERC Undergraduate Student Research Award. The second author was supported by NSERC under grant number 238757.
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References
Dewar, M., Panario, D.: Linear Transformation Shift Registers. IEEE Trans. Inform. Theory 49, 2047–2052 (2003)
Fitzgerald, R.: Irreducible Polynomials Over Finite Fields that are Invariant Under Linear Fractional Transformations (preprint)
Golomb, S.: Shift-Register Sequences. Aegean Park Press (1982)
Tsaban, B., Vishne, U.: Efficient Linear Feedback Shift Registers with Maximal Period. Finite Fields Appl. 8, 256–267 (2002)
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Dewar, M., Panario, D. (2004). Mutual Irreducibility of Certain Polynomials. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds) Finite Fields and Applications. Fq 2003. Lecture Notes in Computer Science, vol 2948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24633-6_5
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DOI: https://doi.org/10.1007/978-3-540-24633-6_5
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