A note on the stability of trinomials over finite fields
نویسندگان
چکیده
منابع مشابه
On the Primitivity of some Trinomials over Finite Fields
In this paper, we give conditions under which the trinomials of the form x + ax + b over finite field Fpm are not primitive and conditions under which there are no primitive trinomials of the form x +ax+b over finite field Fpm . For finite field F4, We show that there are no primitive trinomials of the form x + x + α, if n ≡ 1 mod 3 or n ≡ 0 mod 3 or n ≡ 4 mod 5.
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In this paper, we explore the primitivity of trinomials over small finite fields. We extend the results of the primitivity of trinomials x + ax + b over F4 [1] to the general form x + ax + b. We prove that for given n and k, one of all the trinomials x + ax + b with b being the primitive element of F4 and a + b 6= 1 is primitive over F4 if and only if all the others are primitive over F4. And w...
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In the process of pursuing a finite field analogue of Descartes’ Rule, Bi, Cheng, and Rojas (2014) proved an upper bound of 2 √ q − 1 on the number of roots of a trinomial c1 + c2x a2 + c3x a3 ∈ Fq [x], conditional on the exponents satisfying δ = gcd(a2, a3, q − 1) = 1, and Cheng, Gao, Rojas, and Wan (2015) showed that this bound is near-optimal for many cases. Our project set out to refine the...
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The origin of this work was the search for a “Descartes’ rule” for finite fields a nontrivial upper bound for the number of roots of sparse polynomials. In [2], Bi, Cheng, and Rojas establish such an upper bound. Then, in [3], Cheng, Gao, Rojas, and Wan show that the bound is essentially optimal in an infinite number of cases by constructing t-nomials with many roots in Fpt . However, the bound...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2020
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2020.101649