THE CONSTRUCTION OF CYCLIC CODES FROM SEQUENCES OVER FINITE FIELDS

• Main Author: Nopendri
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/53657
• Institution: Institut Teknologi Bandung

A cyclic code is a subclass of linear code that has efficient encoding and decoding algorithms. Therefore, this cyclic code has many applications in data storage and communication systems. It causes research on cyclic codes has been made to obtain optimal codes. In the paper C. Ding et al. (2013 and 2014), a cyclic code is constructed from a function that generates sequences over a finite field. Although there is no general pattern for obtaining the constructing polynomials in the construction process, the cyclic code produced by C. Ding et al. (2013 and 2014) is the optimal code. The paper presents several open problems. Some of the problems have been solved by several researchers. This research combines one of the open problems that have been solved by modifying the sequence involved so that the codes obtained are different from previous ones. The method used in this study is the same as C. Ding, et al. (2013 and 2014). The new construction of the cyclic code is obtained by generating a sequence with a new definition. The definition of this sequence involves the trace function and nonlinear functions and their properties. In this process, the minimal polynomial of the sequence is determined as well as the generator polynomial of a cyclic code. The final process in this research is to determine the parameters of the codes obtained. This research aims to obtain periodic sequences, linear span, and minimal polynomials from new sequences. This minimal polynomial is the generator polynomial of the cyclic code. Some examples of the code are given, and some of the computation results are shown in the appendix. To see how good the code is, the examples are compared to the existing linear code collection table. Although the presented examples’ results are not optimal, a lower bound of this family of cyclic code can be obtained.