Abstract
We produce a new family of polynomials $f(X)$ over fields $k$ of characteristic $2$ which are exceptional, in the sense that $f(X)-f(Y)$ has no absolutely irreducible factors in $k[X,Y]$ except for scalar multiples of $X-Y$; when $k$ is finite, this condition is equivalent to saying that the map $\alpha\mapsto f(\alpha)$ induces a bijection on an infinite algebraic extension of $k$. Our polynomials have degree $2^{e-1}(2^e-1)$, where $e>1$ is odd. We also prove that this completes the classification of indecomposable exceptional polynomials of degree not a power of the characteristic.
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ISSN = {0925-1022},
CODEN = {DCCREC},
MRCLASS = {05B10 (11T71 94A60)},
MRNUMBER = {2001c:05027},
DOI = {10.1023/A:1008397209409},
ZBLNUMBER = {1056.05024},
}
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