Matrislerin genelleştirilmiş tersleri ve kodlama teorisine uygulamaları

This thesis deals with the application of generalized inverses of matrices over finite fields and the method of least squares in linear codes. It is proven that if the Moore-Penrose inverse of a generator matrix of a linear code exists, a unique word approaching to a received word near the codewords of the code can be found. Together with the introduction, this thesis consists of six chapters. In the first chapter, historical development of generalized inverses is mentioned, shortly. In the second chapter, existence, construction and characterization of generalized inverses of matrices and their relation with linear systems are given. In the last section of chapter two, minimal properties of generalized inverses are investigated. In the third chapter, importantant properties of generalized inverses over finite fields, which are used as our tool to get our results in the fifth chapter, are described. The fourth chapter provides a brief description on error correcting codes and basic definitions in coding theory. In the fifth chapter, the concept of generalized inverses over finite fields and least square solutions applied to the codes. In the final chapter, the conclusion of this dissertation is given.