Optical orthogonal codes: their bounds and new optimal constructions

A (v, k, λ_a, λ_c) optical orthogonal code (OOC) C is a family of (0, 1)-sequences of length v and weight k satisfying the following two correlation properties: (1) Σ_0⩽t⩽v-1x_tx_t+i ⩽λ_a for any x=(x₀,x₁,···,x_v-1 )∈C and any integer i not equivalent 0 mod v; and (2) Σ _0⩽t⩽v-1x_ty_t+i⩽λ _b for any x=(x₀,x₁,···, x_v-1) ∈ C, y=(y₀,y₁,···,y_v-1) ∈C with x≠y, and any integer i, where the subscripts are taken modulo v. The study of optical orthogonal codes is motivated by an application in optical code-division multiple-access communication systems. In this paper, upper bounds on the size of an optical orthogonal code are discussed. Several new constructions for optimal optical orthogonal codes with weight k⩾4 and correlation constraints λ_a=λ_c=1 are described by means of optimal cyclic packings. Many new infinite series of such optimal optical orthogonal codes are thus produced