Computational algebra (2013/2014)

Course code
4S001098
Credits
6
Coordinator
Francesca Mantese
Academic sector
MAT/02 - ALGEBRA
Language of instruction
English
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
Teoria 5 I semestre Francesca Mantese
Esercitazioni 1 I semestre Francesca Mantese

Lesson timetable

I semestre
Activity Day Time Type Place Note
Teoria Tuesday 11:30 AM - 1:30 PM lesson Lecture Hall M  
Teoria Thursday 9:30 AM - 10:30 AM lesson Lecture Hall M  
Esercitazioni Thursday 10:30 AM - 11:30 AM practice session Lecture Hall M  

Learning outcomes

The course provides an introduction to coding theory, presenting the main notions and techniques for error detection and correction. Moreover, some concepts and results from algebra, which are needed in coding theory, are recalled and further developed.

Syllabus

Tools from algebra: groups, rings, fields, classification of finite fields, roots of unity, cyclotomic polynomials, factorization in irreducible polynomials.
Introduction to coding theory. Linear codes. Weights and distances. Error detection and correction. Shannon's Theorem.
Cyclic codes. BCH codes. Reed-Solomon codes. Goppa codes. Quaternary codes. Arithmetic codes. Codes over Z4

Assessment methods and criteria

The exam consists on a written examination and of an optional oral examination.

Teaching aids
Title Format (Language, Size, Publication date)
Appello 03/02/14  pdfpdf (it, 74 KB, 03/03/14)
Appello 24/02/14  pdfpdf (it, 39 KB, 03/03/14)
homeworks  pdfpdf (it, 64 KB, 23/10/13)
Homeworks 2  pdfpdf (it, 49 KB, 31/12/13)