- +902323293535-3743
Zeynep Ödemiş Özger
Izmir Katip Celebi, Engineering Sciences, Faculty Member
- Combinatorics, Coding Theory, Abstract Algebra, Mathematics, Cryptography, Graph Theory, and 12 moreNumber Theory, Algebra, Computer Science, Engineering Sciences, Algebraic Coding Theory, Education, Engineering, Information Technology, Technology, Computer Engineering, Higher Education, and E-learningedit
Research Interests:
Formally self-dual codes and their construction methods have been popular among researchers in the last decade since these codes can have better parameters than self-dual codes can have. The idea of construction methods started with a few... more
Formally self-dual codes and their construction methods have been popular among researchers in the last decade since these codes can have better parameters than self-dual codes can have. The idea of construction methods started with a few examples for binary codes found in [1] and then it is developed by numerous researchers using different rings [2], [3], [4], [5]. Some constructions for binary codes from [1] are proven to be valid for every ring of characteristic 2 in [2]. In this work, formally self-dual codes over S4 = F2 + uF2 + uF2 + uF2 and some of their construction methods similar to the ones in [2] are considered. In [6] cyclic and constacyclic codes over this ring were studied based on a newly defined Gray map and Lee weight. Unlike the Gray map defined in [2] the Gray map introduced here is not duality-preserving, however the MacWilliams identities, having been proven for the Lee weight enumerators, the binary images of formally selfdual codes over S4 are also formally s...
In this study, we present a link between approximation theory and summability methods by constructing bivariate Bernstein-Kantorovich type operators on an extended domain with reparametrized knots. We use a statistical convergence type... more
In this study, we present a link between approximation theory and summability methods by constructing bivariate Bernstein-Kantorovich type operators on an extended domain with reparametrized knots. We use a statistical convergence type and power series method to obtain certain Korovkin type theorems, and we study certain rates of convergences related to these summability methods. Furthermore, we numerically analyze the theoretical results and provide some computer graphics to emphasize the importance of this study.
Research Interests:
We consider codes over $\mathbb{Z}_{p^s}$ with the extended Lee weight. We find Singleton bounds with respect to this weight and define MLDS and MLDR codes accordingly. We also consider the kernels of these codes and the notion of... more
We consider codes over $\mathbb{Z}_{p^s}$ with the extended Lee weight. We find Singleton bounds with respect to this weight and define MLDS and MLDR codes accordingly. We also consider the kernels of these codes and the notion of independence of vectors in this space. We investigate the linearity and duality of the Gray images of codes over $\mathbb{Z}_{p^s}$.
We consider codes over $\mathbb{Z}_{p^s}$ with the extended Lee weight. We find Singleton bounds with respect to this weight and define MLDS and MLDR codes accordingly. We also consider the kernels of these codes and the notion of... more
We consider codes over $\mathbb{Z}_{p^s}$ with the extended Lee weight. We find Singleton bounds with respect to this weight and define MLDS and MLDR codes accordingly. We also consider the kernels of these codes and the notion of independence of vectors in this space. We investigate the linearity and duality of the Gray images of codes over $\mathbb{Z}_{p^s}$.
In this work, linear codes over Z 2 s are considered together with the extended Lee weight that is defined as w L (x) = x if x ≤ 2 s−1 , 2 s − x if x > 2 s−1. The ideas used by Wilson and Yıldız are employed to obtain di-visibility... more
In this work, linear codes over Z 2 s are considered together with the extended Lee weight that is defined as w L (x) = x if x ≤ 2 s−1 , 2 s − x if x > 2 s−1. The ideas used by Wilson and Yıldız are employed to obtain di-visibility properties for sums involving binomial coefficients and the extended Lee weight. These results are then used to find bounds on the power of 2 that divides the number of codewords whose Lee weights fall in the same congruence class modulo 2 e. Comparisons are made with the results for the trivial code and the results for the homogeneous weight.
Research Interests:
We consider codes over Z p s with the extended Lee weight. We find Singleton bounds with respect to this weight and define MLDS and MLDR codes accordingly. We also consider the kernels of these codes and the notion of independence of... more
We consider codes over Z p s with the extended Lee weight. We find Singleton bounds with respect to this weight and define MLDS and MLDR codes accordingly. We also consider the kernels of these codes and the notion of independence of vectors in this space. We investigate the linearity and duality of the Gray images of codes over Z p s .
Research Interests:
In this work, linear codes over the ring S4 = F2 + uF2 + u2F2 + u3F2 are considered. The Lee weight and gray map for codes over S4 are defined and MacWilliams identities for the complete, the symmetrized and the Lee weight enumerators are... more
In this work, linear codes over the ring S4 = F2 + uF2 + u2F2 + u3F2 are considered. The
Lee weight and gray map for codes over S4 are defined and MacWilliams identities for the complete, the
symmetrized and the Lee weight enumerators are obtained. Cyclic and (1 + u2)-constacyclic codes over
S4 are studied, as a result of which a substantial number of optimal binary codes of di↵erent lengths are
obtained as the Gray images of cyclic and constacyclic codes over S4.
Lee weight and gray map for codes over S4 are defined and MacWilliams identities for the complete, the
symmetrized and the Lee weight enumerators are obtained. Cyclic and (1 + u2)-constacyclic codes over
S4 are studied, as a result of which a substantial number of optimal binary codes of di↵erent lengths are
obtained as the Gray images of cyclic and constacyclic codes over S4.