A classification of linear codes based on algebraic structures and Local Cyclic Codes

In this paper, a view point of classification of linear codes based on algebraic structure and Local Cyclic Codes is presented. Linear codes are divided into two types (structural and non-structural); almost all these codes are used widely in practice. Local Cyclic Codes are described in relation with other linear codes. These codes are constructed on decompositions of polynomial ring according to the cyclic multiplicative groups. Traditional cyclic codes are considered as a subclass of Local Cyclic Codes.