A Fast Algorithm for Testing Reducibility of Trinomials
نویسندگان
چکیده
منابع مشابه
A fast algorithm for testing reducibility of trinomials mod~2 and some new primitive trinomials of degree 3021377
The standard algorithm for testing reducibility of a trinomial of prime degree r over GF(2) requires 2r + O(1) bits of memory. We describe a new algorithm which requires only 3r/2+O(1) bits of memory and significantly fewer memory references and bit-operations than the standard algorithm. If 2r − 1 is a Mersenne prime, then an irreducible trinomial of degree r is necessarily primitive. We give ...
متن کاملA Fast Algorithm for Testing Irreducibility of Trinomials
The standard algorithm for testing reducibility of a trinomial of prime degree r over GF(2) requires 2r+O(1) bits of memory and Θ(r) bit-operations. We describe an algorithm which requires only 3r/2 + O(1) bits of memory and significantly fewer bit-operations than the standard algorithm. Using the algorithm, we have found 18 new irreducible trinomials of degree r in the range 100151 ≤ r ≤ 70005...
متن کاملÍòòòóöñ Êêòòóñ Aeùñö Òòööøóö× Òò Èööññøøú Ìööòóñññð×
Generators and Primitive Trinomials Ri hard P. Brent Computing Laboratory University of Oxford rpb omlab.ox.a .uk 1 May 2001 To be presented at OUCL, 1 May 2001. Copyright 2001, R. P. Brent. oxford3t Abstra t In this talk, whi h des ribes joint work with Samuli Larvala and Paul Zimmermann, we onsider the problem of testing trinomials over GF(2) for irredu ibility or primitivity. In parti ular, ...
متن کاملAn Algorithm for Generating Irreducible Cubic Trinomials over Prime Field
This paper proposes an algorithm for generating irreducible cubic trinomials in the form x + ax + b, b ∈ Fp, where a is a certain fixed non-zero element in the prime field Fp. The proposed algorithm needs a certain irreducible cubic trinomial over Fp to be previously given as a generator; however, the proposed algorithm can generate irreducible cubic polynomials one after another by changing a ...
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 کامل