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arXiv · 1311.1366

Divisibility of Trinomials by Irreducible Polynomials over F2

Ryul Kim·Wolfram Koepf
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Abstract

Irreducible trinomials of given degree n over $F_2$ 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 $F_2$. A condition for divisibility of self-reciprocal trinomials by irreducible polynomials over $F_2$ is established. And we extend Welch's criterion for testing if an irreducible polynomial divides trinomials $x^m+x^s+1$ to the trinomials $x^{am}+x^{bs}+1$.

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Ryul Kim, Wolfram Koepf. 2014-01-29. Divisibility of Trinomials by Irreducible Polynomials over F2. https://arxiv.org/abs/1311.1366

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