Corrigenda to ``New primitive $t$-nomials $(t=3,5)$ over $GF(2)$ whose degree is a Mersenne exponent,'' and some new primitive pentanomials
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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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...
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Let D = (V ,E) be a primitive digraph. The local exponent of D at a vertex u ∈ V , denoted by exp D (u), is defined to be the least integer k such that there is a directed walk of length k from u to v for each v ∈ V . Let V = {1, 2, . . ., n}. The vertices of V can be ordered so that exp D (1) 6 exp D (2) 6 · · · 6 exp D (n) = γ (D). We define the kth local exponent set En(k) := {expD(k) | D ∈ ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2002
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-02-01487-4