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n-dimensional optical orthogonal codes, bounds and optimal constructions

  • T. L. AldersonEmail author
Original Paper
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Abstract

We generalize to higher dimensions the notions of optical orthogonal codes. We establish upper bounds on the capacity of general n-dimensional OOCs, and on ideal codes (codes with zero off-peak autocorrelation). The bounds are based on the Johnson bound, and subsume bounds in the literature. We also present two new constructions of ideal codes; one furnishes an infinite family of optimal codes for each dimension \( n\ge 2 \), and another which provides an asymptotically optimal family for each dimension \( n\ge 2 \). The constructions presented are based on certain point-sets in finite projective spaces of dimension k over GF(q) denoted PG(kq).

Keywords

Optical orthogonal code Johnson bound OOC Constant weight codes Singer group 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of New Brunswick Saint JohnSaint JohnCanada

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