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Composition behaviour of sub-linearised polynomials over a finite field. (English) Zbl 1126.11344

Mullin, Ronald C. (ed.) et al., Finite fields: theory, applications, and algorithms. Fourth international conference, Waterloo, Ontario, Canada, August 12–15, 1997. Providence, RI: American Mathematical Society (ISBN 0-8218-0817-6/pbk). Contemp. Math. 225, 67-75 (1999).
From the text: Let \(F\) be a finite field with characteristic \(p\). A linearised polynomial \(L\) over \(F\) is simply an additive polynomial and so has the form \(L(X)=\sum^n_{i=0}z_iX^{p^i}\). Sub-linearised polynomials \(S\), introduced by the reviewer [J. Aust. Math. Soc., Ser. A 49, No. 2, 309–318 (1990; Zbl 0728.11065)], are natural “twists” of linearised polynomials: typically \(L^d(X)=S(X^d)\) for some integer \(d\). It is shown that a decomposable sub-linearised polynomial can be written as the composition of sub-linearised polynomials. Other results connect the decomposition of sub-linearised and linearised polynomials.
For the entire collection see [Zbl 0899.00028].

MSC:

11T06 Polynomials over finite fields

Citations:

Zbl 0728.11065
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