Geometric constructions of optimal optical orthogonal codes

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November 2008, 2(4): 451-467. doi: 10.3934/amc.2008.2.451

Geometric constructions of optimal optical orthogonal codes

T. L. Alderson ^1, and K. E. Mellinger ^2,

1.	Department of Mathematical Sciences, University of New Brunswick Saint John, New Brunswick, E2L 4L5, Canada
2.	Department of Mathematics, University of Mary Washington, 1301 College Avenue, Trinkle Hall, Fredericksburg, VA 22401, United States

Received July 2008 Revised September 2008 Published November 2008

Abstract
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We provide a variety of constructions of $(n, w, \lambda)$-optical orthogonal codes using special sets of points and Singer groups in finite projective spaces. In several of the constructions, we are able to prove that the resulting codes are optimal with respect to the Johnson bound. The optimal codes exhibited have $\lambda = 1, 2$ and $w-1$ (where $w$ is the weight of each codeword in the code). The remaining constructions are are shown to be asymptotically optimal with respect to the Johnson bound, and in some cases maximal. These codes represent an improvement upon previously known codes by shortening the length. In some cases the constructions give rise to variable weight OOCs.

Keywords: conic, Optical orthogonal code, root subline, singer, CDMA.

Mathematics Subject Classification: Primary: 94B27; Secondary: 05B25, 51E99.

Citation: T. L. Alderson, K. E. Mellinger. Geometric constructions of optimal optical orthogonal codes. Advances in Mathematics of Communications, 2008, 2 (4) : 451-467. doi: 10.3934/amc.2008.2.451

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