کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5771540 | 1630354 | 2018 | 11 صفحه PDF | دانلود رایگان |
The well-known Chowla and Zassenhaus conjecture, proved by Cohen in 1990, states that if p>(d2â3d+4)2, then there is no complete mapping polynomial f in Fp[x] of degree dâ¥2. For arbitrary finite fields Fq, a similar non-existence result was obtained recently by IÅık, TopuzoÄlu and Winterhof in terms of the Carlitz rank of f.Cohen, Mullen and Shiue generalized the Chowla-Zassenhaus-Cohen Theorem significantly in 1995, by considering differences of permutation polynomials. More precisely, they showed that if f and f+g are both permutation polynomials of degree dâ¥2 over Fp, with p>(d2â3d+4)2, then the degree k of g satisfies kâ¥3d/5, unless g is constant. In this article, assuming f and f+g are permutation polynomials in Fq[x], we give lower bounds for the Carlitz rank of f in terms of q and k. Our results generalize the above mentioned result of IÅık et al. We also show for a special class of permutation polynomials f of Carlitz rank nâ¥1 that if f+xk is a permutation over Fq, with gcdâ¡(k+1,qâ1)=1, then kâ¥(qân)/(n+3).
Journal: Finite Fields and Their Applications - Volume 49, January 2018, Pages 132-142