منابع مشابه
On Primitive Trinomials (Mode 2), II
The present paper is a completion of a previous paper of the same title (Zierler and Brillhart, 1968). In our preceding work 187 of the irreducible trinomials T~.k(x) = x" ~ x k ~1 were left to be tested for primitivity at a later date, even though the requisite complete factorizations of 2 ~ 1 were known (these trinomials were identified in (Zierler and Brillhart, 1968) by a superscript minus ...
متن کاملA 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 کاملTwelve New Primitive Binary Trinomials
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...
متن کاملTen new primitive binary trinomials
We exhibit ten new primitive trinomials over GF(2) of record degrees 24 036 583, 25 964 951, 30 402 457, and 32 582 657. This completes the search for the currently known Mersenne prime exponents. Primitive trinomials of degree up to 6 972 593 were previously known [4]. We have completed a search for all known Mersenne prime exponents [7]. Ten new primitive trinomials were found. Our results ar...
متن کاملAlgorithms for Finding Almost Irreducible and Almost Primitive Trinomials
Consider polynomials over GF(2). We describe efficient algorithms for finding trinomials with large irreducible (and possibly primitive) factors, and give examples of trinomials having a primitive factor of degree r for all Mersenne exponents r = ±3 mod 8 in the range 5 < r < 10, although there is no irreducible trinomial of degree r. We also give trinomials with a primitive factor of degree r ...
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ژورنال
عنوان ژورنال: Information and Control
سال: 1968
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(68)90973-x