Hermitian Rank Metric Codes and Duality

2021-01-01
La Cruz, Javier De
Evilla, Jorge Robinson
Özbudak, Ferruh
In this paper we define and study rank metric codes endowed with a Hermitian form. We analyze the duality for F-q2-linear matrix codes in the ambient space (F-q2)(n,m) and for both F-q2-additive codes and F-q2m-linear codes in the ambient space F-q2m(n). Similarly, as in the Euclidean case we establish a relationship between the duality of these families of codes. For this we introduce the concept of q(m)-duality between bases of F-q2m over F-q2 and prove that a q(m)-self dual basis exists if and only if m is an odd integer. We obtain connections on the dual codes in F-q2m(n) and (F-q2)(n,m) with the corresponding inner products. In particular, we study Hermitian linear complementary dual, Hermitian self-dual and Hermitian self-orthogonal codes in F-q2m(n) and (F-q2)(n,m). Furthermore, we present connections between Hermitian F-q2-additive codes and Euclidean F-q2-additive codes in F-q2m(n)

Suggestions

Multinormed semifinite von Neumann algebras, unbounded operators and conditional expectations
Dosi, Anar (Elsevier BV, 2018-10-01)
The present paper is devoted to classification of multinormed W*-algebras in terms of their bounded parts. We obtain a precise description of the bornological predual of a multinormed W*-algebra, which is reduced to a multinormed noncommutative L-1-space in the semifinite case. A multinormed noncommutative L-2-space is obtained as the union space of a commutative domain in a semifinite von Neumann algebra. Multinormed W*-algebras of type I are described as locally bounded decomposable (unbounded) operators ...
K-way partitioning of signed bipartite graphs
Ömeroğlu, Nurettin Burak; Toroslu, İsmail Hakkı; Department of Computer Engineering (2012)
Clustering is the process in which data is differentiated, classified according to some criteria. As a result of partitioning process, data is grouped into clusters for specific purpose. In a social network, clustering of people is one of the most popular problems. Therefore, we mainly concentrated on finding an efficient algorithm for this problem. In our study, data is made up of two types of entities (e.g., people, groups vs. political issues, religious beliefs) and distinct from most previous works, sig...
Two dimensional finite volume weighted essentially non-oscillatory euler schemes with uniform and non-uniform grid coefficients
Elfarra, Monier Ali; Akmandor, İbrahim Sinan; Department of Aerospace Engineering (2005)
In this thesis, Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) codes for one and two-dimensional discretised Euler equations are developed. The construction and application of the FV-WENO scheme and codes will be described. Also the effects of the grid coefficients as well as the effect of the Gaussian Quadrature on the solution have been tested and discussed. WENO schemes are high order accurate schemes designed for problems with piecewise smooth solutions containing discontinuities. The key ...
Non-normal bivariate distributions: estimation and hypothesis testing
Qunsiyeh, Sahar Botros; Tiku, Moti Lal; Department of Statistics (2007)
When using data for estimating the parameters in a bivariate distribution, the tradition is to assume that data comes from a bivariate normal distribution. If the distribution is not bivariate normal, which often is the case, the maximum likelihood (ML) estimators are intractable and the least square (LS) estimators are inefficient. Here, we consider two independent sets of bivariate data which come from non-normal populations. We consider two distinctive distributions: the marginal and the conditional dist...
Gödel's metric and its generalization
Özgören, Kıvanç; Karasu, Atalay; Department of Physics (2005)
In this thesis, firstly the original Gödel's metric is examined in detail. Then a more general class of Gödel-type metrics is introduced. It is shown that they are the solutions of Einstein field equations with a physically acceptable matter distribution provided that some conditions are satisfied. Lastly, some examples of the Gödel-type metrics are given.
Citation Formats
J. D. La Cruz, J. R. Evilla, and F. Özbudak, “Hermitian Rank Metric Codes and Duality,” IEEE ACCESS, pp. 38479–38487, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/89457.