A Permutation of a Small Infinite Field

Stephen D. Cohen ()
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Stephen D. Cohen: University of Glasgow, Department of Mathematics

A chapter in Finite Fields and Applications, 2001, pp 109-112 from Springer

Abstract: Abstract Let $$ \mathbb{F} $$ denote the infinite field that is the union of all extensions of GF(2) of odd degree. Let q = 2 m and let $$ {\mathbb{F}_{Q}} = GF(2{q^{2}}) $$ . We provide a simple proof of the permutation property of the polynomials x 2q+1 + x 3 +x on $$ {\mathbb{F}_{Q}} $$ for each m by viewing each member of the class as the action of a simply defined permutation of $$ \mathbb{F} $$ .

Keywords: 11T06; 11T30 (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-3-642-56755-1_10

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