MDR CODES OVER Zk

• Main Author: FIRMAN IHSAN (10112070), ADITYA
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/20752
• Institution: Institut Teknologi Bandung

Information transmission becomes the most crucial thing in our world since communication technology is developed. Unfortunately, sometimes it meets problems because every medium creates noises that will change the received information. As the communication technology is becoming more complex, any code which is used to correct and detect error in the information always have to be generalized. The codes, which are in the first place just constructed over felds structure, are generalized then, to be constructed over more extended structure, like rings. This generalization is of course not only applied just to general properties of the codes, but also to more specific properties like Singleton Bounds. In this final project, one of linear codes, the Maximum Distance Separable (MDS) codes, will be generalized to rings structure, which will be called Maximum Distance Respect to Rank (MDR) codes. The observed rings in this project is finite rings Zk, with k is natural numbers. Then, we will observe how this MDR codes can be reconstructed by using Generalized Chinese Remainder Theorem. After that, because the distance function defined in a code is not only Hamming distance, so the other distances, like Lee and Euclidean, will be used to redefine the MDR codes to Maximum Lee Distance Respect to Rank (MLDR) codes and Maximum Euclidean Distance Respect to Rank (MEDR) codes. In the last part, we will see all concrete examples of the codes with length n over Zk met the definition of MLDR and MEDR codes for n and k given.