Table of irreducible polynomials over ${\rm GF}[2]$ of degrees $10$\ through $20$
نویسندگان
چکیده
منابع مشابه
Distribution of irreducible polynomials of small degrees over finite fields
D. Wan very recently proved an asymptotic version of a conjecture of Hansen and Mullen concerning the distribution of irreducible polynomials over finite fields. In this note we prove that the conjecture is true in general by using machine calculation to verify the open cases remaining after Wan’s work. For a prime power q let Fq denote the finite field of order q. Hansen and Mullen in [4, p. 6...
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finite fields, irreducible polynomials A table of low-weight irreducible polynomials over the finite field F2 is presented. For each integer n in the range 2 = n = 10,000, a binary irreducible polynomial f(x) of degree n and minimum posible weight is listed. Among those of minimum weight, the polynomial listed is such that the degree of f(x) – xn is lowest (similarly, subsequent lower degrees a...
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As we will see, modular arithmetic aids in testing the irreducibility of polynomials and even in completely factoring polynomials in Z[x]. If we expect a polynomial f(x) is irreducible, for example, it is not unreasonable to try to find a prime p such that f(x) is irreducible modulo p. If we can find such a prime p and p does not divide the leading coefficient of f(x), then f(x) is irreducible ...
متن کاملConstruction of Irreducible Polynomials over Finite Fields
In this paper we investigate some results on the construction of irreducible polynomials over finite fields. Basic results on finite fields are introduced and proved. Several theorems proving irreducibility of certain polynomials over finite fields are presented and proved. Two theorems on the construction of special sequences of irreducible polynomials over finite fields are investigated in de...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1972
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1972-0313227-5