Primitive trinomials whose degree is a Mersenne exponent
نویسندگان
چکیده
منابع مشابه
New primitive t-nomials (t = 3, 5) over GF(2) whose degree is a Mersenne exponent
All primitive trinomials over GF (2) with degree 859433 (which is the 33rd Mersenne exponent) are presented. They are X859433 +X288477 + 1 and its reciprocal. Also two examples of primitive pentanomials over GF (2) with degree 86243 (which is the 28th Mersenne exponent) are presented. The sieve used is briefly described.
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We exhibit twelve new primitive trinomials over GF(2) of record degrees 42 643 801, 43 112 609, and 74 207 281. In addition we report the first Mersenne exponent not ruled out by Swan’s theorem [10] — namely 57 885 161 — for which none primitive trinomial exists. This completes the search for the currently known Mersenne prime exponents. Primitive trinomials of degree up to 32 582 657 were repo...
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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 ...
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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, ...
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ژورنال
عنوان ژورنال: Information and Control
سال: 1969
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(69)90631-7