Costas arrays, known for their ideal autocorrelation properties, play a vital role in radar, sonar, and communication systems. Traditionally, they are obtained through exhaustive search or algebraic construction. This paper investigates the correlation properties of permutation arrays and examines the structural relationships and cross‐correlation between an original Costas array and those derived from flipping and rotation. Through rigorous mathematical analysis, we establish a series of theorems that precisely characterize these relationships. This framework enhances the understanding of Costas array construction and establishes a solid theoretical foundation for the research and practical applications of Costas arrays.
Yao et al. (Thu,) studied this question.