Determination of the sizes of optimal -OOSPCs for

Optical orthogonal signature pattern codes (OOSPCs) were first introduced by Kitayama in [K. Kitayama, Novel spatial spread spectrum based fiber optic CDMA networks for image transmission, IEEE J. Sel. Areas Commun. 12 (4) (1994) 762–772]. They find application in transmitting a two-dimensional image through multicore fiber in the CDMA communication system. For given positive integers m , n , k , λ a and λ c , let Θ ( m , n , k , λ a , λ c ) denote the largest number of codewords among all ( m , n , k , λ a , λ c ) -OOSPCs. An ( m , n , k , λ a , λ c ) -OOSPC with Θ ( m , n , k , λ a , λ c ) codewords is said to be optimal. In this paper, the number of codewords in an optimal ( m , n , k , λ , k − 1 ) -OOSPC (i.e., the exact value of Θ ( m , n , k , λ , k − 1 ) ) is determined for any positive integers m , n , k and λ = k − 1 , k .