Hamming distances of unsaturated orthogonal arrays

Abstract

Orthogonal arrays (OAs) are applied in the statistical design of experiments, coding theory, cryptography, various types of software testing and quality control and have many connections to other combinatorial designs. The Hamming distances of OAs play a critical role in many areas such as algebraic combinatorics, quantum information theory, and wireless sensor networks. However, the calculation method of Hamming distances is difficult, especially for mixed orthogonal arrays (MOAs), since they rely on constructions or structures of OAs in many cases. In this article, by using the number of coincidences, we find some OAs with high strength and MOAs with strength 2 and 3, whose Hamming distances do not depend on their structures. We also calculate Hamming distances of a series of unsaturated asymmetrical OAs via their construction methods such as deleting columns, the expansive replacement method, and difference schemes.