On the decomposition ofxd+aexe+⋯+a1x+a0
2000 ◽
Vol 23
(11)
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pp. 777-781
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Keyword(s):
LetKdenote a field. A polynomialf(x)∈K[x]is said to be decomposable overKiff(x)=g(h(x))for some polynomialsg(x)andh(x)∈K[x]with1<deg(h)<deg(f). Otherwisef(x)is called indecomposable. Iff(x)=g(xm)withm>1, thenf(x)is said to be trivially decomposable. In this paper, we show thatxd+ax+bis indecomposable and that ifedenotes the largest proper divisor ofd, thenxd+ad−e−1xd−e−1+⋯+a1x+a0is either indecomposable or trivially decomposable. We also show that ifgd(x,a)denotes the Dickson polynomial of degreedand parameteraandgd(x,a)=f(h(x)), thenf(x)=gt(x−c,a)andh(x)=ge(x,a)+c.
Several classes of permutation trinomials from Niho exponents over finite fields of characteristic 3
2019 ◽
Vol 18
(04)
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pp. 1950069
2011 ◽
Vol 60
(4)
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pp. 602-607
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Keyword(s):
2008 ◽
pp. 88-102
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2006 ◽
Vol 2006
◽
pp. 1-6
1987 ◽
Vol 30
(1)
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pp. 19-27
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2008 ◽
pp. 79-90
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Keyword(s):