Bounds and constructions for two-dimensional variable-weight optical orthogonal codes. (English) Zbl 1342.94126
Summary: Optical orthogonal codes (1D constant-weight OOCs or 1D CWOOCs) were first introduced by J. A. Salehi [IEEE Trans. Commun. 37, No. 8, 824–833 (1989); (with C. A. Brackett) ibid. 37, No. 8, 834–842 (1989)] as signature sequences to facilitate multiple access in optical fibre networks. In fiber optic communications, a principal drawback of 1D CWOOCs is that large bandwidth expansion is required if a big number of codewords is needed. To overcome this problem, a two-dimensional (2D) (constant-weight) coding was introduced. Many optimal 2D CWOOCs were obtained recently. A 2D CWOOC can only support a single QoS (quality of service) class. A 2D variable-weight OOC (2D VWOOC) was introduced to meet multiple QoS requirements. A 2D VWOOC is a set of 0, 1 matrices with variable weight, good auto, and cross-correlations. Little is known on the construction of optimal 2D VWOOCs. In this paper, a new upper bound on the size of a 2D VWOOC is obtained, and several new infinite classes of optimal 2D VWOOCs are obtained.
MSC:
| 94B25 | Combinatorial codes |
| 94B65 | Bounds on codes |
| 05B10 | Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) |
| 05B40 | Combinatorial aspects of packing and covering |
Keywords:
optical orthogonal code; skew starter; strictly cyclic packing; 2D variable-weight optical orthogonal codeReferences:
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