Some combinatorial constructions for optical orthogonal codes

Abstract A (v, k, ρ) optical orthogonal code C is a family of (0, 1)-sequences of length v and weight k satisfying the following two properties: (1) ∑0⩽t⩽v−1xtxt + i ⩽ ρ, for any x = (x0, x1, …, xv − 1) ∈ C and any integer i ≢ 0 (mod v); (2) ∑0⩽t⩽v − 1xtyt + i ⩽ ρ, for any x ≠ y in C and any integer i. The study of optical orthogonal codes is motivated by an application in a code-division multiple-access fiber optical channel which requires binary sequences with good correlation properties. In this paper, some combinatorial constructions for optimal (v, k, 1) optical orthogonal codes are developed. The constructions are also used to derive a bulk of new optical orthogonal codes.

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