1. Algebraic System - Basic Concepts, Semi Group, Identity Element and Monoids

In this 50 mins Video Lesson

Introduction, n-ary operation, Algeraic System, Binary Operations, Semi-Group, Residue Class Modulo n, Identity, Monoid, and other topics.

Introduction, n-ary operation, Algeraic System, Binary Operations, Semi-Group, Residue Class Modulo n, Identity, Monoid, and other topics.

2. Inverse, Groups, Abelian Group, Cyclic Group and Cosets

In this 53 mins Video Lesson

Inverse of an Element, Group, Abelian Group, Order of a Group, Order of An element, Cyclic Group, Product Group, Properties of a Group, Sub-Group, Cosets, Properties of a Coset, and other topics.

Inverse of an Element, Group, Abelian Group, Order of a Group, Order of An element, Cyclic Group, Product Group, Properties of a Group, Sub-Group, Cosets, Properties of a Coset, and other topics.

3. Properties of Cosets, Normal Sub Group, Homomorphism, Automorphism, Isomorphism

In this 47 mins Video Lesson

Properties of Cosets (contd...), Lagrange's Theorem, Normal Subgroup, Qotient Group, Group Homomorphism, Group Automorphism, Group Isomorphism, and other topics.

Properties of Cosets (contd...), Lagrange's Theorem, Normal Subgroup, Qotient Group, Group Homomorphism, Group Automorphism, Group Isomorphism, and other topics.

4. Ring, Integral Domain and Fields

In this 52 mins Video Lesson

Rings, Commutative Ring, Ring with no proper Divisors of 0, Ring with a unity, Unit of a Ring, Integral Domain, Field, Properties of Rings, Example, and other topics.

Rings, Commutative Ring, Ring with no proper Divisors of 0, Ring with a unity, Unit of a Ring, Integral Domain, Field, Properties of Rings, Example, and other topics.

5. Ring Homomorphism and Coding Theory

In this 34 mins Video Lesson

Ring Homomorphism and Kernel, Coding Theory, Weight of a code, Distance between codewords, Properties of distance function, and other topics.

Ring Homomorphism and Kernel, Coding Theory, Weight of a code, Distance between codewords, Properties of distance function, and other topics.

6. Coding Theory (Contd.), Generator, Parity Check Matrix and Group Code

In this 41 mins Video Lesson

Generator matrix, Paritycheck matrix, Group Code, Decoding a group code, and other topics.

Generator matrix, Paritycheck matrix, Group Code, Decoding a group code, and other topics.

7. Ring of Polynomial and Cyclic Code

In this 29 mins Video Lesson

Ring of Polynomials, Root, Ring of Polynomial modulo p(x), Ideal in a Ring, Cyclic Code, and other topics.

Ring of Polynomials, Root, Ring of Polynomial modulo p(x), Ideal in a Ring, Cyclic Code, and other topics.

Algebraic System
(5.85 Mb)

Algebraic Systems, Groups, Semi Groups, Monoid, Subgroups, Permutation Groups, Codes and Group codes, Isomorphism and Automorphisms, Homomorphism and Normal Subgroups, Ring, Integral Domain, Field, Ring Homomorphism, Polynomial Rings and Cyclic Code