Work

Construction of orthogonal arrays with repetitions of two distinct rows

Year: 2026

Type: article

Abstract: Orthogonal arrays with repeated rows are applied in various aspects such as statistical experimental design and pure error estimation, quantum information and quantum communication, and scientific computing and computer theory. However, existing research only focuses on an orthogonal array in which a row is repeated, while research on an orthogonal array with repetitions of two distinct rows remains scarce. In this paper, we mainly focus on such an array. As well known, a bound is quite powerful in proving nonexistence. Because of the complexity of its structures, from two aspects we derive a bound for ones of strength 2. Based on this bound, we define optimal, x -optimal and ( x , m 1 , m 2 ) -optimal arrays. We further present a general construction method via difference schemes and obtain a large number of such arrays. Moreover, for the cases of high strength, two efficient construction methods are proposed to produce a large number of new arrays. Some selective arrays are tabulated for practical uses.

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2026.115424

Authors: Jing Wang, Shulan Li, Shanqi Pang, Chen Li, Xiaoyuan Shen

Institutions: Henan Normal University, Shangqiu Normal University

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,320

Funders: National Natural Science Foundation of China, Natural Science Foundation of Henan Province