Obtaining error correcting codes from discrete finite structures

Keywords: Linear codes, t-designs, Hadamard, matrix, projective and affine planes, difference sets, Latin squares, Orthogonal arrays.This study consists of five chapters. In the first chapter, there is information about necessary algebraic definitions, theorems for linear codes.In the second chapter, basic definitions and theorems about design theory are introduced. Moreover, methods for designs are examined and examples related to this are given.In the third chapter, after basic definitions and theorems about projective and affine planes, difference sets and Latin squares are introduced, their relationships between each other and design theory are examined.In the fourth chapter, designs which are obtained from finite vector spaces and examples of these are presented.In the fifth chapter, some codes which are obtained from the design theory are given. Especially the codes which are obtained from the symmetric designs are determined. In addition, the codes which are obtained from Latin squares and Hadamard matrixes are also given. Finally, some examples of codes from designs and vice versa are illustrated.