Combinatorial Constructions For Optical Orthogonal Codes And Related Designs

An optical orthogonal code is a family of sequences with good auto-and cross-correlation properties, which plays an important role in the application of fiber optical code division multiple access (OCDMA) system. The combinatorial design theory such as group divisible design or cyclic packing design is a powerful tool for the constructions of optical orthogonal codes. In this thesis, the semi-cyclic group divisible designs are discussed, and the new infinite classes of optimal variable-weight optical orthogonal codes are established.The thesis is organized as follows.Chapter1gives an introduction on the background of semi-cyclic group divisible designs and variable-weight optical orthogonal codes, and the main result of this thesis.In Chapter2, some auxiliary designs are applied to establish the recursive con-structions for semi-cyclic group divisible designs. Both direct and recursive construc-tions are used to show the necessary and sufficient conditions for the existence of a (3, A)-SCGDD of type gt.In Chapter3, the existence of cyclic packing design are presented by the direct construction method, such as cyclotomic class, skew starter and computer research. With the relationship between cyclic packing designs and optical orthogonal codes, and by the recursive constructions, several infinite classes of optimal variable-weight optical orthogonal codes are established, where the weight is{3,4} or{3,5}.