n-dimensional optical orthogonal codes, bounds and optimal constructions

Abstract

We generalized to higher dimensions the notions of optical orthogonal codes. We establish uper bounds on the capacity of general n-dimensional OOCs, and on specific types of ideal codes (codes with zero off-peak autocorrelation). The bounds are based on the Johnson bound, and subsume many of the bounds that are typically applied to codes of dimension three or less. We also present two new constructions of ideal codes; one furnishes an infinite family of optimal codes for each dimension n ≥ 2, and another which provides an asymptotically optimal family for each dimension n ≥ 2. The constructions presented are based on certain point-sets in finite projective spaces of dimension k over GF (q) denoted P G(k, q).

New Zero Cross-Correlation Codes Based on Zech Method’s for OCDMA Systems

“…In the literature, various code schemes have been proposed to overcome the MAI problem among multiple users for the SAC-OCDMA systems, such as M-sequence codes [12], optical orthogonal codes [13][14][15][16], prime codes [17], double weight codes [18][19][20], and random diagonal (RD) codes [21]. The construction of the code is limited by the code length parameters, as is the case for the modified quadratic congruence [22,23] and Dynamic Cyclic shift codes [1].…”