Işık, Leyla and Topuzoğlu, Alev and Winterhof, Arne (2016) Complete mappings and Carlitz rank. Designs, Codes, and Cryptography . ISSN 09251022 (Print) 15737586 (Online) Published Online First http://dx.doi.org/10.1007/s1062301602935
This is the latest version of this item.
Official URL: http://dx.doi.org/10.1007/s1062301602935
Abstract
The wellknown Chowla and Zassenhaus conjecture, proven by Cohen in 1990, states that for any d≥2 and any prime p>(d2−3d+4)2 there is no complete mapping polynomial in Fp[x] of degree d. For arbitrary finite fields Fq, we give a similar result in terms of the Carlitz rank of a permutation polynomial rather than its degree. We prove that if n<⌊q/2⌋, then there is no complete mapping in Fq[x] of Carlitz rank n of small linearity. We also determine how far permutation polynomials f of Carlitz rank n<⌊q/2⌋ are from being complete, by studying value sets of f+x. We provide examples of complete mappings if n=⌊q/2⌋, which shows that the above bound cannot be improved in general.
Item Type:  Article 

Uncontrolled Keywords:  Permutation polynomials; Complete mappings; Carlitz rank; Value sets of polynomials 
Subjects:  Q Science > QA Mathematics > QA150272.5 Algebra 
Divisions:  Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences 
Depositing User:  Alev Topuzoğlu 
Date Deposited:  09 Sep 2017 21:57 
Last Modified:  09 Sep 2017 21:57 
URI:  https://research.sabanciuniv.edu/id/eprint/33595 
Available Versions of this Item

Complete mappings and Carlitz rank. (deposited 02 Nov 2016 15:16)
 Complete mappings and Carlitz rank. (deposited 09 Sep 2017 21:57) [Currently Displayed]