FINITE FIELDS
cod. 14856

Academic year 2009/10
3° year of course - First semester
Professor
Academic discipline
Algebra (MAT/02)
Field
Formazione algebrico-geometrica
Type of training activity
Characterising
56 hours
of face-to-face activities
6 credits
hub:
course unit
in - - -

Learning objectives

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 unit content

<br />Complements on the derivates of the polynomials, multiple roots, splitting fields. Existence and unicity unless isomorphisms of the finite field of order Pn.<br />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.

Full programme

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Bibliography

M. Girardi, G. Israel 'Teoria dei Campi', Feltrinelli.

Teaching methods

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Assessment methods and criteria

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Other information

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