MSc (Mathematics and Computing) Programme:Algebraic Coding TheoryThapar University
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Real Analysis – I
Fundamentals of Computer Science and C Programming
Discrete Mathematical Structure
Real Analysis –II
Advanced Abstract Algebra
Computer Oriented Numerical Methods
Data Based Management Systems
Computer Based Optimization Techniques
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.