Abstract Algebra and its Application

Scope of questions for State exams of Bachelor's degree program

Branch: Mathematical Physics

Subject: Abstract Algebra and its Application

Subjects regarding the questions:

  • 01ALGE Algebra
  • 01TKO Theory of Codes 
1. Relations, equivalence, ordering
2. Groups, normal subgroups, quotient groups
3. Rings, ideals
4. Divisibility in integral domains
5. Fields, characteristic of a field, prime subfield
6. Finite fields
7. Linear codes, information symbols, systematic codes, Hamming bound, standard decoding
8. Levenshtein theorem, Hadamard matrices and optimal codes
9. Cyclic codes, generating and parity check polynomials
10. Hamming codes, BCH codes