Correcting errors and erased letters using parikh matrices

The Parikh matrix of a word is an upper triangular matrix which contains information on the number of occurrences of certain subwords of that word. More than one word can correspond to the same Parikh matrix. Words that have the same Parikh matrix are called M-equivalent. In this thesis, M-equivalent words are used as codewords to examine the error and erased letter correction capability of the Parikh matrix. This thesis consists of seven chapters. The second chapter contains a literature review, and the third chapter includes basic definitions related to words. Parikh mappings are introduced in the fourth chapter. In the fifth chapter, M-equivalent words and uniformly Parikh-friendly words are presented. In the sixth chapter, which contains the main results of the thesis, it is explained how to correct errors and erased letters using Parikh matrices. The last chapter contains the results and suggestions of the thesis.