MSc (Mathematics and Computing) Programme:Algebraic Coding Theory

Semester I

Real Analysis – I
Linear Algebra
Complex Analysis
Fundamentals of Computer Science and C Programming
Discrete Mathematical Structure
Differential Equations


Semester II

Real Analysis –II
Advanced Abstract Algebra
Computer Oriented Numerical Methods
Data Structures
Data Based Management Systems
Operating Systems


Semester III

Topology
Computer Based Optimization Techniques
Computer Networks
Mechanics
Seminar


Semester IV

Functional Analysis
Dissertation


Algebraic Coding Theory

Introduction to Coding Theory: Code words, distance and weight function, nearest-neighbour decoding principle, Error detection and correction, matrix encoding techniques, matrix codes, group codes, decoding by coset leaders, generator and parity check matrices, syndrom decoding procedure, dual codes.

Linear Codes: Linear codes, matrix description of linear codes, equivalence of linear codes, minimum distance of linear codes, dual code of a linear code, weight distribution of the dual code of a binary linear code, Hamming codes.

BCH Codes: Polynomial codes, finite fields, minimal and primitive polynomials, Bose-Chaudhuri-Hocquenghem codes.

Cyclic Codes: Cyclic codes, algebraic description of cyclic codes, check polynomial, BCH and Hamming codes as cyclic codes.

MDS Codes: Maximum distance separable codes, necessary and sufficient conditions for MDS codes, weight distribution of MDS codes, an existence problem, Reed-Solomon codes..


199.Introduction: Finite element methods, history and range of applications.

Finite Elements: definition and properties, assembly rules and general assembly procedure, features of assembled matrix, boundary conditions.

Continuum problems: classification of differential equations, variational formulation approach, Ritz method, generalized definition of an element, element equations from variations. Galerkin’s weighted residual approach, energy balance methods.

Element shapes and interpolation functions: Basic element shapes, generalized co-ordinates, polynomials, natural co-ordinates in one-, two- and three-dimensions, Lagrange and Hermite polynomials, two-D and three-D elements for Co and C1 problems, Co-ordinate transformation, iso-parametric elements and numerical integration.

Application of Finite Element Methods To Elasticity Problems And Heat Transfer Problems.