Some properties of the cycle decomposition of WG-NLFSR | Zendy

Yujuan Li | Zendy; Huaifu Wang | Zendy; Peipei Zhou | Zendy; Guoshuang Zhang | Zendy

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Some properties of the cycle decomposition of WG-NLFSR

Author(s) -

Yujuan Li,

Huaifu Wang,

Peipei Zhou,

Guoshuang Zhang

Publication year - 2020

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2020050

Subject(s) - mathematics , decomposition , permutation (music) , combinatorics , decomposition theorem , parity (physics) , discrete mathematics , ecology , physics , particle physics , acoustics , biology

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.

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