Constructions of Combinatorial Arrays and Block Designs using Algebraic Curves

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Combinatorial problems like orthogonal arrays, balanced arrays, BIBD, etc, are important themes in mathematics since 18^<th> century. Recently those mathematical problems are great matter of concern in application areas like wireless communication, DNA testing and Finance. In this project, we have aimed to construct those applicable combinatorial arrays and designs using algebraic curves and varieties on finite projective geometries. In 1999, we constructed balanced arrays from algebraic curves using a property of multiplicity. In 2000, we constructed code for optical fiber communications, called optical orthogonal code. For this construction, many algebraic and geometrical properties are used. We also found a construction of balanced arrays using geometrical varieties of quadratic functions over finite field. In 2001, we continued to construct optical orthogonal code. Furthermore, we found some construction of resolvable designs and nested designs.