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The paper describes an algebraic construction of the inversive difference field associated with a discrete-time rational nonlinear control system under the assumption that the system is submersive. We prove that a system is submersive iff its associated difference ideal is proper, prime and reflexive. Next, we show that Kähler differentials of the… (More)

In this paper, we give conditions under which the trinomials of the form x n + ax + b over finite field Fpm are not primitive and conditions under which there are no primitive trinomials of the form x n + ax + b over finite field Fpm. For finite field F4, We show that there are no primitive trinomials of the form x n + x + α, if n ≡ 1 mod 3 or n ≡ 0 mod 3… (More)

Recently, Kalikinkar Mandal and Guang Gong presented a family of nonlinear pseudo-random number generators using Welch-Gong Transformations in their paper [6]. They also performed the cycle decomposition of the WG-NLFSR recurrence relations over different finite fields by computer simulations where the nonlinear recurrence relation is composed of a… (More)

In this paper, we explore the primitivity of trinomials over small finite fields. We extend the results of the primitivity of trinomials x n + ax + b over F4 [1] to the general form x n + ax k + b. We prove that for given n and k, one of all the trinomials x n + ax k + b with b being the primitive element of F4 and a + b = 1 is primitive over F4 if and only… (More)

We present a criterion for the similarity of length-two elements in a noncom-mutative principal ideal domain. The criterion enables us to develop an algorithm for determining whether B 1 A 1 and B 2 A 2 are similar, where A 1 , A 2 , B 1 , B 2 are first-order differential (difference) operators. The main step in the algorithm is to find a rational solution… (More)

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