Further results on balanced \((n, \{3, 4 \}, \Lambda_a, 1)\)-OOCs. (English) Zbl 1372.94479
Summary: Let \(W = \{w_1, \ldots, w_r \}\) be an ordering of a set of \(r\) integers greater than 1, \(\Lambda_a = (\lambda_a^{(1)}, \ldots, \lambda_a^{(r)})\) be an \(r\)-tuple of positive integers, \(\lambda_c\) be a positive integer, and \(Q = (q_1, \ldots, q_r)\) be an \(r\)-tuple of positive rational numbers whose sum is 1. In 1996, Yang introduced variable-weight optical orthogonal code \(((n, W, \Lambda_a, \lambda_c, Q)\)-OOC) for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Most existing works on variable-weight optical orthogonal codes assume that \(\lambda_a^{(1)}, \dots, \lambda_a^{(r)} = \lambda_c = 1\). In this paper, new balanced \((n, \{3, 4 \}, \Lambda_a, 1)\)-OOCs are constructed, where \(\Lambda_a \in \{(1, 2),(2, 1),(2, 2) \}\).
Keywords:
optical orthogonal code; partitionable set; quadratic residue; skew starter; unequal correlation parametersReferences:
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