Akademik Veri Yönetim Sistemi
Tezin Türü: Doktora
Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Türkiye
Tezin Onay Tarihi: 2014
Tezin Dili: İngilizce
Öğrenci: Dilek Çelik
Danışman: FERRUH ÖZBUDAK
Özet:Bent functions over the finite fields of odd characteristics received a lot of attention of late years. Over the finite fields with characteristic 2, a method is given to construct bent functions using near bent functions. This method is then generalized to finite fields with p elements for an odd prime p by Cesmelioglu et al. The idea is constructing a bent function F by glueing the near-bent functions in such a way that Walsh spectrum of F do not include zero value. This can be achieved by combining the near-bent functions having no common element in supports of their Walsh transforms and the union of their support of Walsh transforms should be equal to domain of near-bent functions. In this thesis, we aim to construct regular, weakly regular and non-weakly regular bent functions. For this purpose, we first give an adaptation of the method given in, to the finite fields with p^m elements and ring of integers modulo p^m, where m is a positive integer greater than 1. Then, we generalize the method by using s plateaued functions, for an integer s> 1, instead of using near bent functions over ring of integers modulo p^m. It is notable to emphasize that, we obtain completely different results in every adaptation process.To apply the method of construction, we compute the Walsh spectrum of quadratic functions over finite fields with p^m elements and ring of integers modulo p^m. We evaulate the quadratic Gauss sum over Z_q to achieve the computation over the ring of integers. Also, we give a technique to classify the constructed bent functions as regular, weakly regular and non weakly regular.