Computational methods in coding theory (original) (raw)
2010
This project will attempt an in-depth study of algebraic coding theory. We will study the two basic kinds of codes: Block codes and trellis codes. Specifically, we will look at linear block codes, cyclic codes, Hamming codes, and convolutional codes.
Algorithmic issues in coding theory
Lecture Notes in Computer Science, 1997
The goal of this article is to provide a gentle introduction to the basic definitions, goals and constructions in coding theory. In particular we focus on the algorithmic tasks tackled by the theory. W e describe some of the classical algebraic constructions of error-correcting codes including the Hamming code, the Hadamard code and the Reed Solomon code. We describe simple proofs of their error-correction properties. We also describe simple and e cient algorithms for decoding these codes. It is our aim that a computer scientist with just a basic knowledge of linear algebra and modern algebra should be able to understand every proof given here. We also describe some recent developments and some salient open problems.
A perspective on coding theory
Information Sciences, 1991
The field of error correcting codes has developed rapidly over the past forty years. During the past decade in particular two very significant developments have occurred and these are briefly reviewed here. From this basis, suggestions are made as to where coding principles might find application in the future.
Algebraic Coding Theory in the Quest for Efficient Digital India
The objective of this paper is to demonstrate the application of Algebraic Coding towards achievement of "Efficiency" of this huge Central Government Initiative.Digital India is a Government of India initiative with the vision to transform economy of India using digital technologies and to make India ready for a knowledge-based future. One of the key factors that influencing the success of this programme shall be its "Efficiency".
Reasoning about coding theory: The benefits we get from computer algebra
1998
The use of computer algebra is usually considered beneficial for mechanised reasoning in mathematical domains. We present a case study, in the application domain of coding theory, that supports this claim: the mechanised proofs depend on non-trivial algorithms from computer algebra and increase the reasoning power of the theorem prover. The unsoundness of computer algebra systems is a major problem in interfacing them to theorem provers.
Achieving Reliable Digital Data Communication through Mathematical Algebraic Coding Techniques
2016
The Objective of this paper is to demonstrate the application of “Mathematical Algebraic Coding Techniques” in quest of achieving “Reliable Digital Data Communication Systems”. Environmental interference and physical defects in any digital data communication system can cause random bit errors during data transmission. As the signal is transmitted through a communication system, the signal gets corrupted because of noise and distortion. In another words, the communication system may not be reliable due to the aforesaid reasons.