Explicit class field theory for rational function fields

Zikan, Abdelhalim


Explicit Full Correlation Distribution of Sequence Families Using Plateaued Functions
BOZTAŞ, Serdar; Özbudak, Ferruh; TEKİN, Eda (2018-04-01)
The design of code division multiple access sequence families dates back to the Gold sequences from the 1960s. Since then there has been a number of different such designs with good correlation properties, some optimal and some near-optimal. In this paper, we use the concept of plateaued functions with arbitrary degree, in order to compute their full correlation distributions. First, we give an explicit correlation distribution of a sequence family using a non-quadratic function. Then for the quadratic func...
Explicit evaluation of Walsh transforms of a class of Gold type functions
Cosgun, Ayhan (2018-03-01)
Let K = F-2(k) denote the finite field of 2(k) elements. The Walsh transform of a class of Gold type functions f(x) = Tr-K (x(2a+1) + x(2b+1)), 0 <= a < b at alpha is an element of K is determined in recent results of Lahtonen et al. (2007) [7], Roy (2012) [10] and Cosgun et al. (2016) [2] under some restrictions on k, a, b and a. In this paper, we give explicit evaluation of the Walsh transforms off without any restriction on k, a, b and alpha. Therefore we improve and generalize the related results in lit...
Explicit Characterizations for Plateaued-ness of p-ary (Vectorial) Functions
CARLET, CLAUDE; MESNAGER, SİHEM; Özbudak, Ferruh; SINAK, AHMET (2017-04-12)
Plateaued (vectorial) functions have an important role in the sequence and cryptography frameworks. Given their importance, they have not been studied in detail in general framework. Several researchers found recently results on their characterizations and introduced new tools to understand their structure and to design such functions. In this work, we mainly extend some of the observations made in characteristic 2 and given in (Carlet, IEEE Trans. Inf. Theor. 61(11), 6272- 6289, 2015) to arbitrary characte...
Explicit maximal and minimal curves over finite fields of odd characteristics
Özbudak, Ferruh (2016-11-01)
In this work we present explicit classes of maximal and minimal Artin-Schreier type curves over finite fields having odd characteristics. Our results include the proof of Conjecture 5.9 given in [1] as a very special subcase. We use some techniques developed in [2], which were not used in [1].
Explicit maximal and minimal curves over finite fields of odd characteristics
Özbudak, Ferruh (null; 2015-04-13)
Citation Formats
A. Zikan, “Explicit class field theory for rational function fields,” Middle East Technical University, 1989.