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.

中文翻译：

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WG-NLFSR循环分解的一些性质

在本文中，我们给出了由Mandal和Gong提出的非线性反馈移位寄存器WG-NLFSR的循环分解的一些性质。首先我们给出WG-NLFSR的状态转换变换的奇偶性，然后通过第1节定理2中给出的置换奇偶性与它的周期数的关系，我们表明的循环分解中的周期数WG-NLFSR是偶数。其次，当特征多项式的系数属于定义了WG-NLFSR的有限域的适当子域时，我们研究WG-NLFSR的循环分解性质。最后，我们给出了过滤WG7-NLFSR的循环分解的一些属性。