New construction of binary and nonbinary quantum stabilizer codes based on symmetric matrices

2019 ◽  
Vol 33 (24) ◽  
pp. 1950274 ◽  
Author(s):  
Duc Manh Nguyen ◽  
Sunghwan Kim
Keyword(s):  
Inner Product ◽  
Symmetric Matrices ◽  
Parity Check ◽  
Stabilizer Codes ◽  
Construction Methods ◽  
Singleton Bound ◽  
New Construction ◽  
Symplectic Inner Product ◽  
Quantum Stabilizer Codes

In this paper, we propose two construction methods for binary and nonbinary quantum stabilizer codes based on symmetric matrices. In the first construction, we use the identity and symmetric matrices to generate parity-check matrices that satisfy the symplectic inner product (SIP) for the construction of quantum stabilizer codes. In the second construction, we modify the first construction to generate parity-check matrices based on the Calderbank–Shor–Stean structure for the construction of quantum stabilizer codes. The binary and nonbinary quantum stabilizer codes whose parameters achieve equality of the quantum singleton bound are investigated with the code lengths ranging from 4 to 12.

scholarly journals New Constructions of Quantum Stabilizer Codes Based on Difference Sets

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 655 ◽  
Author(s):  
Duc Nguyen ◽  
Sunghwan Kim
Keyword(s):  
Difference Sets ◽  
Combinatorial Design ◽  
Inner Product ◽  
Code Construction ◽  
Stabilizer Codes ◽  
Stabilizer Code ◽  
The Difference ◽  
Symplectic Inner Product ◽  
Quantum Stabilizer Code ◽  
Quantum Stabilizer Codes

In this paper, new conditions on parameters in difference sets are derived to satisfy symplectic inner product, and new constructions of quantum stabilizer codes are proposed from the conditions. The conversion of the difference sets into parity-check matrices is first explained. Then, the proposed code construction is composed of three steps, which are to choose the generators of quantum stabilizer code, to determine the quantum stabilizer groups, and to determine subspace codewords with large minimum distance. The quantum stabilizer codes with various length are also presented to explain the practicality of the code construction. The proposed design can be applied to quantum stabilizer code construction based on combinatorial design.

Quantum stabilizer codes based on a new construction of self-orthogonal trace-inner product codes over GF(4)

2020 ◽  
Vol 34 (05) ◽  
pp. 2050017 ◽  
Author(s):  
Duc Manh Nguyen ◽  
Sunghwan Kim
Keyword(s):  
Linear Codes ◽  
Galois Field ◽  
Inner Product ◽  
Quantum Codes ◽  
Product Codes ◽  
Stabilizer Codes ◽  
Comparison Results ◽  
Construction Of Self ◽  
New Construction ◽  
Quantum Stabilizer Codes

In this paper, we propose quantum stabilizer codes based on a new construction of self-orthogonal trace-inner product codes over the Galois field with 4 elements (GF(4)). First, from any two binary vectors, we construct a generator matrix of linear codes whose components are over GF(4). We prove that the proposed linear codes comply with the self-orthogonal, trace-inner product. Then, we propose mapping tables to construct new quantum stabilizer codes by using linear codes. Comparison results show that our proposed quantum codes have various dimensions for any code length with the capacity for better errors correction relative to the referenced quantum codes.

A method of constructing fuzzy implications from the FIφ-construction

2021 ◽  
pp. 1-14
Author(s):  
Yifan Zhao ◽  
Kai Li
Keyword(s):  
Specific Property ◽  
New Method ◽  
Aggregation Function ◽  
Fuzzy Implications ◽  
Construction Methods ◽  
Fuzzy Implication ◽  
New Construction

In the recent years, several new construction methods of fuzzy implications have been proposed. However, these construction methods actually care about that the new implication could preserve more properties. In this paper, we introduce a new method for constructing fuzzy implications based on an aggregation function with F (1,  0) =1, a fuzzy implication I and a non-decreasing function φ, called FIφ-construction. Specifically, some logical properties of fuzzy implications preserved by this construction are studied. Moreover, it is studied how to use the FIφ-construction to produce a new implication satisfying a specific property. Furthermore, we produce two new subclasses of fuzzy implications such as UIφ-implications and GpIφ-implications by this method and discuss some additional properties. Finally, we provide a way to generate fuzzy subsethood measures by means of FIφ-implications.

Next Generation CANDU: Conceptual Design for a Short Construction Schedule

2002 ◽  
Author(s):  
Jerry M. Hopwood ◽  
Ian J. W. Love ◽  
Medhat Elgohary ◽  
Neville Fairclough
Keyword(s):  
Conceptual Design ◽  
Critical Path ◽  
Construction Method ◽  
Phase Iii ◽  
Next Generation ◽  
Project Schedule ◽  
Construction Methods ◽  
New Construction ◽  
Construction Strategy ◽  
Construction Schedule

Atomic Energy of Canada Ltd. (AECL) has very successful experience in implementing new construction methods at the Qinshan (Phase III) twin unit CANDU 6 plant in China. This paper examines the construction method that must be implemented during the conceptual design phase of a project if short construction schedules are to be met. A project schedule of 48 months has been developed for the nth unit of NG (Next Generation) CANDU with a 42 month construction period from 1st Concrete to In-Service. An overall construction strategy has been developed involving paralleling project activities that are normally conducted in series. Many parts of the plant will be fabricated as modules and be installed using heavy lift cranes. The Reactor Building (RB), being on the critical path, has been the focus of considerable assessment, looking at alternative ways of applying the construction strategy to this building. A construction method has been chosen which will result in excess of 80% of internal work being completed as modules or as very streamlined traditional construction. This method is being further evaluated as the detailed layout proceeds. Other areas of the plant have been integrated into the schedule and new construction methods are being applied to these so that further modularization and even greater paralleling of activities will be achieved. It is concluded that the optimized construction method is a requirement, which must be implemented through all phases of design to make a 42 month construction schedule a reality. If the construction methods are appropriately chosen, the schedule reductions achieved will make nuclear more competitive.

Some new construction methods for t-norms on bounded lattices

2019 ◽  
Vol 48 (7) ◽  
pp. 775-791 ◽  
Author(s):  
Ümit Ertuğrul ◽  
M. Nesibe Kesicioğlu ◽  
Funda Karaçal
Keyword(s):  
Construction Methods ◽  
New Construction
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