On the cycle structure of certain classes of nonlinear shift registers

Cheng, Unjeng

doi:10.1016/0097-3165(84)90019-0

Cited by 8 publications

(7 citation statements)

References 4 publications

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“…4of Section II, we prove that the sequences generated by these NFSRs have the least periods dividing n(q + 1) and this generalizes some results in Ref. [13].…”

Section: Introductionsupporting

confidence: 82%

“…Cheng in Ref. [13] discussed the periods of the sequences generated by an n-stage NFSR with feedback function…”

Section: So the Subspace B *mentioning

confidence: 99%

“…is a linear combination of only odd (or only even) elementary symmetric functions on the variables [13] . It was proved that in this case the proposed NFSR sequences have the least periods dividing n(q+1).…”

Section: Introductionmentioning

confidence: 99%

“…[9] and Ref. [13], we analyse the periods of the proposed NFSR sequences in this paper by computing the order of the restriction of δ f to some subspace of B n . Indeed, a subspace of B n spanned by a finite set of Boolean functions is constructed such that the order δ f can be calculated by restricting δ f to it.…”

Section: Introductionmentioning

confidence: 99%

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The Periods of a Class of Nonlinear Feedback Shift Register Sequences

Liang

Zeng

2016

Chin. j. electron.

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“…4of Section II, we prove that the sequences generated by these NFSRs have the least periods dividing n(q + 1) and this generalizes some results in Ref. [13].…”

Section: Introductionsupporting

confidence: 82%

“…Cheng in Ref. [13] discussed the periods of the sequences generated by an n-stage NFSR with feedback function…”

Section: So the Subspace B *mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Periods of a Class of Nonlinear Feedback Shift Register Sequences

Liang

Zeng

2016

Chin. j. electron.

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“…In the theory of NLFSRs, the property of the cycle decomposition of NLFSRs is an important property to look at first, since each cycle can be considered as a sequence and the length of the cycle determines the period of the sequence. For more details on the study results of the cycle decomposition of NLFSRs, one can refer to [2,4,6,7,9,10].…”

Section: Introductionmentioning

confidence: 99%

Some properties of the cycle decomposition of WG-NLFSR

Li¹,

Wang²,

Zhou³

et al. 2021

Advances in Mathematics of Communications

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In this paper, we give some properties of the cycle decomposition of a nonlinear feedback shift register called WG-NLFSR which was presented by Mandal and Gong recently. First we give the parity of the state transition transformation of WG-NLFSR and then by the relation of the parity of a permutation and its number of cycles given in Theorem 2 in Section 1, we show that the number of cycles in the cycle decomposition of WG-NLFSR is even. Second we study the properties of the cycle decomposition of WG-NLFSR when the coefficients of the characteristic polynomial belong to the proper subfields of the finite field on which the WG-NLFSR is defined. Finally, we give some properties of the cycle decomposition of the filtering WG7-NLFSR.2010 Mathematics Subject Classification: 94A55, 94A60.

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Further results on the equivalence between Galois NFSRs and Fibonacci NFSRs

Zhao

Zhang

2019

Des. Codes Cryptogr.

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On the cycle structure of certain classes of nonlinear shift registers

Cited by 8 publications

References 4 publications

The Periods of a Class of Nonlinear Feedback Shift Register Sequences

The Periods of a Class of Nonlinear Feedback Shift Register Sequences

Some properties of the cycle decomposition of WG-NLFSR

Further results on the equivalence between Galois NFSRs and Fibonacci NFSRs

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