A class of permutation trinomials over finite fields

Xiang-dong Hou

Xiang-dong Hou

Acta Arithmetica, Tome 166 (2014), p. 51-64 / Harvested from The Polish Digital Mathematics Library

Résumé

Let q > 2 be a prime power and $f = - x + t x^{q} + x^{2 q - 1}$ , where $t \in *_{q}$ . We prove that f is a permutation polynomial of $_{q ²}$ if and only if one of the following occurs: (i) q is even and $T r_{q / 2} (1 / t) = 0$ ; (ii) q ≡ 1 (mod 8) and t² = -2.

Publié le : 2014-01-01

Zbl 1294.11210

EUDML-ID : urn:eudml:doc:286516

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     author = {Xiang-dong Hou},
     title = {A class of permutation trinomials over finite fields},
     journal = {Acta Arithmetica},
     volume = {166},
     year = {2014},
     pages = {51-64},
     zbl = {1294.11210},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-1-3}
}

Xiang-dong Hou. A class of permutation trinomials over finite fields. Acta Arithmetica, Tome 166 (2014) pp. 51-64. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-1-3/