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.

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.

Compensatory and dispensatory measures Disability/Invalidity/Specific Learning Disorder

Dispensatory measures and compensatory tools are intended to enable students to achieve the same learning objectives as their fellow students, not to facilitate the examination.

The use of compensatory tools and the application of dispensatory measures must be authorised in advance by the teacher in agreement with the Referee.

To take advantage of the adaptations during the examination, fill in the Adaptation request form; the request will be automatically sent by the system to the teacher in charge of the teaching, to the Contact Person of your School/Area/Department and in copy to the Sector; you will also receive a copy of the request sent by e-mail.

The adjustments available to students are as follows:

• Additional time (+30% DSA)

• Additional time (+50% disability/invalidity)

• Additional time during oral exams to organise the answer

• Calculator (programmable and graphing calculators are not allowed)

• Conceptual Maps

• Tables and/or Forms

• Take the exam in written form

• Take the exam in oral form

• Tutor reader (for written tests only)

• Tutor-writer (for written tests only)

Your request for adaptations must be submitted at least 7 working days before the scheduled exam date.

All information for students with disabilities and DSA is available on the webpage: Services for students with disabilities or DSA | UniGe | University of Genoa

Reference for inclusion: Sergio Di Domizio - sergio.didomizio@unige.it