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arXiv · 1812.04294

A Swan-like note for a family of binary pentanomials

Giorgos Kapetanakis
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Abstract

In this note, we employ the techniques of Swan (Pacific J. Math. 12(3): 1099-1106, 1962) with the purpose of studying the parity of the number of the irreducible factors of the penatomial $X^n+X^{3s}+X^{2s}+X^{s}+1\in\mathbb{F}_2[X]$, where $s$ is even and $n>3s$. Our results imply that if $n \not\equiv \pm 1 \pmod{8}$, then the polynomial in question is reducible.

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Giorgos Kapetanakis. 2018-12-11. A Swan-like note for a family of binary pentanomials. https://arxiv.org/abs/1812.04294

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