有限域上的本原变换移位寄存器
Primitive transformation shift registers over finite fields
摘要：
本文研究了任意有限域上n阶本原TSR的存在性和计数问题。本文证明了特征为2的有限域上二阶本原TSR的存在性，并建立了本原TSR与特殊形式的本原多项式之间的等价关系。我们提出了关于这些特殊类型的本原多项式存在性的猜想，并进行了一些实验验证。此外，我们还试图枚举本原TSR的特点二有限域上的二阶。最后给出了任意有限域上奇阶本原TSR的一般搜索算法，特别是特征为2的域上二阶本原TSR的一般搜索算法。
英文摘要：
We consider the problem of existence and enumeration of primitive TSRs of order n over any finite field. Here we prove the existence of primitive TSRs of order two over finite fields of characteristic two and establish an equivalence between primitive TSRs and primitive polynomials of special form. A conjecture regarding the existence of these special type of primitive polynomials is submitted by us along with some experimental verification. Further we have attempted to enumerate primitive TSRs of order two over finite fields of characteristic two. Finally we give a general search algorithm for primitive TSRs of odd order over any finite field and in particular of order two over fields of characteristic two.
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