CONSTRUCTION OF LINEAR CODES OVER Z2M + VZ2M

• Main Author: Rosdiana, Sri
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/53072
• Institution: Institut Teknologi Bandung

Research on codes over rings started in early 1970. This research was motivated by the existence of Gray map whose image gives codes over fields. This map preserves distance. Another topic in code over rings concerning MacWilliams identity. The MacWilliams identity relates Hamming weight enumerator from linear code with its dual. MacWilliams identity has wide application, especially in self-dual code which is an important class of linear codes. A self-dual code has a property that its weight distribution is the same as its dual. With this property, a wider class of codes known as formally self-dual code can be defined, that includes self-dual codes. Besides self-dual codes, another important class of linear code is Maximum Distance Separable (MDS) codes and cyclic codes. A code which satisfies the Singleton Bound is called an MDS code. A code is called cyclic of length n over R if it can be represented as an ideal in R[x] xn?1 . We study the structure of the ring R = Z2m + vZ2m, where v2 = v and construct codes over R. From this structure we verify whether this ring is a finite chain ring or not, we investigate MacWilliams identity for the complete weight enumerator on linear code over ring R, we also introduce self-dual codes, we investigate existence of MDS codes. Moreover, we investigate cyclic codes and constacyclic codes particular over Z8 + vZ8.