Factorization of Trinomials over Galoisfields
ثبت نشده
چکیده
We study the parity of the number of irreducible factors of trinomials over Galois elds of characteristic 2. As a consequence , some suucient conditions for a trinomial being reducible are obtained. For example, x n + ax k + b 2 GF (2 t))x] is reducible if both n; t are even, except possibly when n = 2k, k odd. The case t = 1 was treated by R.G.Swan 10], who showed that x n + x k + 1 is reducible over GF (2) if 8jn.
منابع مشابه
A Multi-level Blocking Distinct Degree Factorization Algorithm
We give a new algorithm for performing the distinct-degree factorization of a polynomial P (x) over GF(2), using a multi-level blocking strategy. The coarsest level of blocking replaces GCD computations by multiplications, as suggested by Pollard (1975), von zur Gathen and Shoup (1992), and others. The novelty of our approach is that a finer level of blocking replaces multiplications by squarin...
متن کاملDivisibility of Trinomials by Irreducible Polynomials over F_2
Irreducible trinomials of given degree n over F2 do not always exist and in the cases that there is no irreducible trinomial of degree n it may be effective to use trinomials with an irreducible factor of degree n. In this paper we consider some conditions under which irreducible polynomials divide trinomials over F2. A condition for divisibility of selfreciprocal trinomials by irreducible poly...
متن کاملOn 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.
متن کاملSeveral Classes of Permutation Trinomials over $\mathbb F_{5^n}$ From Niho Exponents
The construction of permutation trinomials over finite fields attracts people’s interest recently due to their simple form and some additional properties. Motivated by some results on the construction of permutation trinomials with Niho exponents, by constructing some new fractional polynomials that permute the set of the (q + 1)-th roots of unity in Fq2 , we present several classes of permutat...
متن کاملOn the Primitivity of Trinomials over Small Finite Fields
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997