Construction of Asymmetric Orthogonal Arrays of Strength Three via a Replacement Method

Zhang, Tian-fang; Deng, Qiaoling; Dey, A.

doi:10.1002/jcd.21557

Cited by 15 publications

(2 citation statements)

References 9 publications

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“…Recently, many new methods of constructing OAs have been provided, and many new classes of OAs have been obtained (Chen et al, 2014; Chen & Niu, 2023; Hedayat et al, 1999; He et al, 2022; Pang & Chen, 2017; Pang, Lin, & Wang, 2018a; Pang, Wang, Lin, & Liu, 2021a; Wang et al, 2019; Zhang et al, 1999, 2016, 2017; Zhang et al, 2001). With deep research on OAs, they are applied to coding theory (Bierbrauer, 2005; Byrne & Sney, 2016), communication (Gao et al, 2017), cryptography (Carlet et al, 2023; Pang, Wang, et al, 2018b), quantum information (Goyeneche et al, 2016; Lin & Jimbo, 2014; Pang, Zhang, Du, & Wang, 2021b; Pang, Zhang, Fei, & Zheng, 2021c; Pang et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

On the construction of nested orthogonal arrays with the adjacent numbers of levels

Pang,

Zhu

2024

Stat

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Nested orthogonal arrays (NOAs) provide an option for designing an experimental setup consisting of two experiments, with the expensive higher‐precision experiment nested within a larger and relatively inexpensive lower‐precision experiment. Construction of NOAs with the adjacent numbers of levels is a challenging problem. In this paper, we present several methods for constructing such NOAs and obtain some classes of such new symmetric NOAs in which the larger arrays have minimum run size. These methods are also extended to construction of NOAs with more than two layers. Furthermore, by adding some columns to these symmetric NOAs, we can construct a lot of new asymmetric NOAs. Illustrative examples are given.

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Section: Introductionmentioning

confidence: 99%

On the construction of nested orthogonal arrays with the adjacent numbers of levels

Pang,

Zhu

2024

Stat

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“…We will denote such an array by OA

. Recently, many new methods of constructing OAs, especially high strength OAs, have been presented, and many new classes of OAs have been obtained [ 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 ]. An OA

is said to be an irredundant orthogonal array (IrOA) if, in any

subarray, all of its rows are different [ 18 ].…”

Section: Introductionmentioning

confidence: 99%

Construction of Binary Quantum Error-Correcting Codes from Orthogonal Array

Pang

Xu²,

Chen³

2022

Entropy

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By using difference schemes, orthogonal partitions and a replacement method, some new methods to construct pure quantum error-correcting codes are provided from orthogonal arrays. As an application of these methods, we construct several infinite series of quantum error-correcting codes including some optimal ones. Compared with the existing binary quantum codes, more new codes can be constructed, which have a lower number of terms (i.e., the number of computational basis states) for each of their basis states.

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Construction of Asymmetric Orthogonal Arrays With High Strength

Lin,

Pang,

Wang

2024

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Orthogonal arrays (OAs) are a key research focus in combinatorial design theory and experimental design theory. They play a very important role in an increasing number of interdisciplinary fields, such as computer science, cryptography, multipartite quantum states and quantum information. And the open problems in many fields are closely related to the construction of orthogonal arrays with high strength and large size. At present, some open problems have been solved by using orthogonal arrays. There is an urgent need for developing such orthogonal arrays. This article introduces a general method for obtaining asymmetric orthogonal arrays with high strength. The proposed method is straightforward and constructive. The constructed OAs can be utilized to generate more OAs. Some selective OAs are tabulated for practical applications.

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Construction of Asymmetric Orthogonal Arrays of Strength Three via a Replacement Method

Abstract: A replacement procedure to construct orthogonal arrays of strength three was proposed by Suen et al. [7]. This method was later extended by Suen and Dey [8]. In this paper, we further explore the replacement procedure to obtain some new families of orthogonal arrays of strength three.

Cited by 15 publications

References 9 publications

On the construction of nested orthogonal arrays with the adjacent numbers of levels

On the construction of nested orthogonal arrays with the adjacent numbers of levels

Construction of Binary Quantum Error-Correcting Codes from Orthogonal Array

Construction of Asymmetric Orthogonal Arrays With High Strength

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