MTC-231 :
Groups and Coding Theory
Unit 1. Integers [05 Lectures]
1.1 Division Algorithm (without Proof),
1.2 G.C.D. using division algorithm and expressing it as linear combination
1.3 Euclid’s lemma
1.4 Equivalence relation (revision), Congruence relation on set of integers, Equivalence class partition
Unit 2. Groups [03 Lectures]
2.1 Binary Operation
2.2 Group: Definition and Examples
2.3 Elementary Properties of Groups
Unit 3. Finite Groups and Subgroups [10 Lectures]
3.1 Order of a group, order of an element
3.2 Examples (Zn, +) and (U(n), *)
3.3 Subgroup definition, Finite subgroup test, subgroups of Zn
3.4 Generator, cyclic group, finding generators of Zn( Corollary 3,4 without proof)
3.5 Permutation group, definition, composition of two permutations, representation
as product of disjoint cycles, inverse and order of a permutation, even/ odd permutation
3.6 Cosets: Definition, Examples and Properties, Lagrange Theorem(without Proof)
Unit 4. Groups and Coding Theory [18 Lectures]
4.1 Coding of Binary Information and Error detection
4.2 Decoding and Error Correction
4.3 Public Key Cryptography
Text Books:-
1. Contemporary Abstract Algebra By J. A, Gallian (Seventh Edition)
Unit 1:Chapter 0, Unit 2: Chapter 2, Unit 3: Chapter 3 ,4, 5 and 7
2. Discrete Mathematical Stuctures By Bernard Kolman, Robert C. Busby and Sharon
Ross (6th Edition) Pearson Education Publication Unit 4: Chapter 11
Use following link for previous year question papers of BCA
Use following link for previous year question papers of B.Sc (Computer Science)
FYBSc(Cyber and Digital Science) question paper
Notes of Digital Communication and Networking
