Topics covered in the class
Sept. 11: Introduction, Fields.
Sept. 13: Characteristic, Binomial Theorem, Prime fields.
Sept. 18: Isomorphism, prime fields, polynmials.
Sept. 20: Polynomial rings, Division algorithm , Euclidean algorithm
Sept. 25: gcd, irreducible polynomials, unique factorization, residue class rings
Sept. 27: Residue class fields, fields extensions.
Assign#1 is out.
Oct. 2: Fields extensions.
Oct. 4: Linear codes.
Oct. 9: Linear codes.
Oct. 11: Syndrome and Hamming codes. Multiplicative group of a finite field
Oct. 16: primitive elements, Gauss algorithm, size of a finite field.
Oct. 18: Mobius functions, existence of irreducible polynomials
Oct. 23: existence of irreducible polynomials
Oct. 25: subfields, automorphisms, characteristic polynomials, minimal polynomials.
Oct. 30: minimial polynomials, primitive polynomials
Nov. 1: midterm
Nov. 6: review, Trace and Norm.
Nov. 8 Trace and Norm, Berlekamp's algorithm
Nov. 13. Berlekamp's algorithm
Nov. 15. factorization of x^n -1.
Nov. 20. cyclic codes.
Nov. 23. Cyclic codes, double error correcting BCH codes,
Nov. 25. double error correcting BCH codes, BCH codes with designed distance
Nov. 28. BCH codes, Reed-Solomon codes.