OVERVIEW

This is an introductory course in Coding Theory.

The course will be dedicated to the mathematical aspects of Coding Theory which studies the problem of correcting errors in messages transmitted through a non secure channel with noise.

AIMS AND CONTENT

LEARNING OUTCOMES

The aim of the course is to provide knowledge of the main concepts and tools of coding theory.

AIMS AND LEARNING OUTCOMES

At the end of the course students will be able to:

- recognise the main classes of error correcting codes;
- master the main constructions of linear codes;
- recognise the principal decoding algorithms.

PREREQUISITES

Necessary prerequisites are the following: vector spaces, groups, fields.

The courses "Algebra Lineare e Geometria Analitica" and "Algebra 2" are recommended.

TEACHING METHODS

Lectures.

SYLLABUS/CONTENT

- introduction to the problem of error-correction in data transmission; 
- linear codes over finite fields;
- Hamming distance and minimum distance decoding;
- perfect and MDS codes;
- Hamming codes;
- codes constructions;
- cyclic codes;
- Goppa codes

- Code-based criptography

- codes on algebraic curves

RECOMMENDED READING/BIBLIOGRAPHY

J.H Van Lint - Introduction to coding theory

H.C.A. van Tilborg - Coding Theory,  a first course

Caminata, De Negri - Notes of the course 

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

The class will start according to the academic calendar.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Oral exam.

Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.

See  https://2023.aulaweb.unige.it/course/view.php?id=12490#section-3 for further information.

ASSESSMENT METHODS

Questions of the oral exam will concern the main topics presented during the lectures. The aim is to establish not only whether students will have reached an appropriate level of knowledge, but also whether they can analize and approach problems related to Coding Theory.

FURTHER INFORMATION

Attendance is recommended.