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CODE THEORY

CODE 34327
ACADEMIC YEAR 2022/2023
CREDITS
  • 6 cfu during the 1st year of 9011 MATEMATICA(LM-40) - GENOVA
  • 7 cfu during the 2nd year of 9011 MATEMATICA(LM-40) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/02
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 2° Semester
    TEACHING MATERIALS AULAWEB

    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 present the basic topics 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

    Coding Theory:
     

    - 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 elliptic curves

    RECOMMENDED READING/BIBLIOGRAPHY

    J.H Van Lint - Introduction to coding theory

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

    TEACHERS AND EXAM BOARD

    Exam Board

    EMANUELA DE NEGRI (President)

    ALDO CONCA

    ALESSIO CAMINATA (President Substitute)

    LESSONS

    LESSONS START

    The class will start according to the academic calendar.

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    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.

    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.