Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algorithms for Finding Almost Irreducible and Almost Primitive
  Trinomials   Consider polynomials over ${\rm GF}(2)$. 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 $r = \pm 3 \bmod 8$ in the range $5 < r < 10^7$, although
there is no irreducible trinomial of degree $r$. We also give trinomials with a
primitive factor of degree $r = 2^k$ for $3 \le k \le 12$. These trinomials
enable efficient representations of the finite field ${\rm GF}(2^r)$. We show
how trinomials with large primitive factors can be used efficiently in
applications where primitive trinomials would normally be used.

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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int