2-dimensional optical orthogonal codes from singer groups |
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Authors: | TL Alderson Keith E Mellinger |
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Institution: | aDepartment of Mathematical Sciences, University of New Brunswick Saint John, Saint John, NB, E2L 4L5, Canada;bDepartment of Mathematics, University of Mary Washington, 1301 College Avenue, Trinkle Hall, Fredericksburg, VA 22401, USA |
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Abstract: | We present several new families of (Λ×T,w,λ) (2D) wavelength/time optical orthogonal codes (2D-OOCs) with λ=1,2. All families presented are either optimal with respect to the Johnson bound (J-optimal) or are asymptotically optimal. The codes presented have more flexible dimensions and weight than the J-optimal families appearing in the literature. The constructions are based on certain pointsets in finite projective spaces of dimension k over GF(q) denoted PG(k,q). This finite geometries framework gives structure to the codes providing insight. We establish that all 2D-OOCs constructed are in fact maximal (in that no new codeword may be added to the original whereby code cardinality is increased). |
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Keywords: | Singer cycle 2-dimensional optical orthogonal code OCDMA |
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