Further results on optimal $ (n, \{3, 4, 5\}, \Lambda_a, 1, Q) $-OOCs

Abstract

Let $ W = \{w_1, w_2, \cdots, w_r\} $ be a set of $ r $ integers greater than 1, $ \Lambda_a = (\lambda_a^{(1)}, \lambda_a^{(2)}, \cdots, \lambda_a^{(r)}) $ be an $ r $-tuple of positive integers, $ \lambda_c $ be a positive integer, and $ Q = (q_1, q_2, \cdots, q_r) $ be an $ r $-tuple of positive rational numbers whose sum is 1. Variable-weight optical orthogonal code ($ (n, W, \Lambda_a, \lambda_c, Q) $-OOC) was introduced by Yang for multimedia optical CDMA systems with multiple quality of service requirements. In this paper, tight upper bounds on the maximum code size of $ (n, \{3, 4, 5\}, \Lambda_a, 1, Q) $-OOCs are obtained, and infinite classes of optimal $ (n, \{3, 4, 5\}, \Lambda_a, 1, Q) $-OOCs are constructed.