Some Classes of Repeated-root Constacyclic Codes for Multi-symbol Read Channels and Applications

Authors

Madhu Kant Thakur

Indian Institute of Technology (ISM), Dhanbad, Jharkhand

DOI: https://doi.org/10.21467/thesis.183

Synopsis

The main objective of coding theory is to find codes with efficient encoding and decoding techniques and the greatest possible value of distance for a given code length, code size, and code alphabet cardinality. Various distances like Hamming distances, symbol-pair distances, etc., have been established and investigated in coding theory to analyse a code’s error-detecting and error-correcting capabilities with respect to various communication channels. A maximum distance separable code (MDS code) is a code that meets the Singleton bound. The MDS codes have the greatest error correcting capability. When the length and size of the codes are fixed, an MDS code has the largest distance. As a result, nowadays, researching and discovering MDS codes with respect to various distances is a hot topic in coding theory. In the theory of error-correcting codes, constacyclic codes over finite fields play a crucial role. Constacyclic codes, moreover, have many real-world applications. Shift registers can effectively encode and decode these codes because they have rich algebraic structures. They also offer excellent error-correction capabilities. All of this clarifies their chosen engineering role. In this monograph, we determine the multi-symbol distances of various classes of repeated-root constacyclic codes over some classes of finite commutative chain rings and investigate various classes of non-trivial MDS codes using these multi-symbol distance distributions.

Keywords: Thesis