Explicit Constructions of Cyclic Packing and Their Related OOCs

Abstract

Since their desirable features, variable-weight optical orthogonal codes (VWOOCs) have found wide ranges of applications in various optical networks and systems. In recent years, optimal \(2\)-CP\((W, 1, Q; n)\)s are used to construct optimal VWOOCs. So far, some works have been done on optimal \(2\)-CP\((W, 1, Q; n)\)s with \(w_{\max} \leq 6\), where \(w_{\max} = \max\{w: w \in W\}\). As far as the authors are aware, little is known for explicit constructions of optimal \(2\)-CP\((W, 1, Q; n)\)s with \(w_{\max} \geq 7\) and \(|W| = 3\). In this paper, two explicit constructions of \(2\)-CP\((\{3, 4, 7\}, 1, Q; n)\)s are given, and two new infinite classes of optimal VWOOCs are obtained.