Oct 4: 2-error-correcting BCH codes (introduction).
Definition of finite fields and prime finite fields.
Polynomials over finite fields. Examples. Irreducible polynomials
and their importance in finite fields. Unique factorization.
Oct 6: Decoding algorithm for 2-error-correcting BCH codes.
Primitive elements. Representation of elements using primitive
elements. Example of decoding procedure.
Oct 18:
Review. Rings and fields. Finite fields have prime characteristic.
Properties. The ring of polynomials. Division algorithm. Euclidean
algorithm. Examples. Ideals. Extension fields. Splitting fields.
Oct 20: Characterization of finite fields. The number of
elements of a finite field. Existence and uniqueness of finite
fields. Subfield criterion.
[A2 handed out.]
Oct 25: Subfield criterion (cont). The multiplicative
group of the nonzero elements in a finite field is cyclic.
Primitive elements. Comments about Assignment 2.
[A1 handed in.]
Oct 27: Midterm test.