$(m\kern -1pt,n\kern -1pt,3\kern -1pt,1)$ Optical Orthogonal Signature Pattern Codes With Maximum Possible Size

Abstract

Kitayama proposed a novel code-division multiple-access (CDMA) network for image transmission called spatial CDMA. Optical orthogonal signature pattern codes (OOSPCs) have attracted wide attention as signature patterns of spatial CDMA. An (m,n,k,λ)-OOSPC is a set of m × n (0,1)-matrices with Hamming weight k and maximum correlation value λ. Let Θ (m,n,k,λ) be the largest possible number of codewords among all (m,n,k,λ) -OOSPCs. In this paper, we concentrate on the calculation of the exact value of Θ (m,n,3,1) and the construction of an (m,n,3,1)-OOSPC with Θ (m,n,3,1) codewords. As a consequence, we show that Θ (m,n,3,1)=[ mn-1/6]-1 when mn≡ 14, 20(mod 24), or mn≡ 8, 16(mod 24) and gcd (m,n,4)=2 , or mn≡ 2(mod 6) and gcd (m,n,4)=4 , and Θ (m,n,3,1)= [mn-1/6] otherwise.