Fields and codes 1987/88.

For 4th year mathematics students. Official name: Algebra superiore.

EXTENSIONOS OF FIELDS The minimal subfield in a field Algebraic and transcendental elements Adjunction of roots Algebraic extensions GALOIS THEORY Recalling some results in group theory Groups of permutations Splittings fields and normal extensions The Galois group Symmetric polynomials Fundamental theorem of Galois theory Extension of homomorphisms Normality theorems FINITE FIELDS The group of invertible elements of a field Finite extensions of a finite field The field with 16 elements Existence and unicity of finite fields INTRODUCTION TO THE THEORY OF CODES Fundamental concepts Linear algebra Linear codes Cyclic codes Polynomial division