Linear Codes Over Finite Chain Rings With Respect To The Rosenbloom-Tsfasman Metric

The Rosenbloom-Tsfasman (shortly RT) metric is a non hamming metric which can be used in uniform distributions and be propitious to know the structure of the codes.M.Yu.Rosenbloom and M.A Tsfasman defined the RT metric over fields in 1977.Some scholars studied the RT metric over fields and obtained a lot of importance results. The research of linear code about RT metric over fields has already been completed . In the recent years the scholars majored in codes shift the interesting from fields to rings. Mehmet Ozen and Man Siap studied the property of linear codes about RT metric over F_q[u]/(u^s).In this paper we generalized the result of F_q[u]/(u^s) to finite chain rings ,especially to quaternary rings.This dissertation is divided into five parts as follows.In chapter one, we briefly review the development of algebraic coding theory and mention main results of this paper.In chapter two, we introduce the concepts needed in paper, especially introduce the the Rosenbloom-Tsfasman metric.The chapter three is the first main part of the dissertation. we studied the property of linear and cyclic codes about RT metric over finite chain rings.The chapter four is the second main part of the dissertation. we study the property of linear codes about RT metric overZ₄ and F₂ + uF₂.In chapter five ,we summarize the main findings in this paper, and bring forward several issues worthy of further study.