Hermitian Rank Metric Codes and Duality

Date

2021-01-01

Author

La Cruz, Javier De
Evilla, Jorge Robinson
Özbudak, Ferruh

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

243
views

0
downloads

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)

URI

https://hdl.handle.net/11511/89457

Journal

IEEE ACCESS

DOI

https://doi.org/10.1109/access.2021.3064503

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

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...
Exceptional Lie algebra g2 and its representations Kayakökü, Mehmet Mustafa; Ünal, İbrahim; Department of Mathematics (2022-9-01) In the classification of complex simple Lie algebras, there are five of them whose Dynkin diagrams are of exceptional type. The Lie algebra g_2 has the smallest dimension among these exceptional Lie algebras and together with its corresponding Lie group G_2, it plays an important role in differential geometry, mathematical physics, and modern string theory. In this thesis after a general introduction to Lie algebras, we show the classification of complex simple ones. Afterward, we give several constructions...
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...

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.