FINITE FIELDS
ACADEMIC YEAR2009/2010
COD. 14856
dati insegnamento:
DEGREE: MATEMATICA E INFORMATICA
TYPE OF COURSE: COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
LECTURERS:
GALLINA Giordano
ACADEMIC YEAR: 2009/2010
YEAR OF STUDY: 3
SEMESTER: First semester
NUMBER OF CREDITS: 6
UNIT COORDINATOR: GALLINA Giordano
CONTACT HOURS:
Learning outcomes of the course unit
To give a deepening of the argument "Finite fields" beginned in the first year, argument which has applications in the theory of codes, in the finite geometries, in the combinatorics.
Prerequisites
Course of Algebra
Course contents summary
Complements on the derivates of the polynomials, multiple roots, splitting fields. Existence and unicity unless isomorphisms of the finite field of order Pn.
Subfields of the finite fields. Roots of the irreducible polynomials. Automorphisms. Norms and traces. Cyclotomic polynomials. The function of Möbius in the theory of finite fields. Orders of the polynomials with coifficients in finite field. Algorithm of Berlekamp. Algorithm of Zassenhaus.
Recommended readings
M. Girardi, G. Israel 'Teoria dei Campi', Feltrinelli.
