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 12 publications

(1 citation statement)

References 9 publications

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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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“…We will denote such an array by 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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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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Constructions for new orthogonal arrays based on large sets of orthogonal arrays

Chen

Niu

2023

Des. Codes Cryptogr.

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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 12 publications

References 9 publications

Construction of Binary Quantum Error-Correcting Codes from Orthogonal Array

Construction of Binary Quantum Error-Correcting Codes from Orthogonal Array

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

Constructions for new orthogonal arrays based on large sets of orthogonal arrays

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