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Syllabus ( MATH 419 )


   Basic information
Course title: Introduction to Coding Theory
Course code: MATH 419
Lecturer: Assist. Prof. Roghayeh HAFEZIEH
ECTS credits: 6
GTU credits: 3 (3+0+0)
Year, Semester: 4, Fall and Spring
Level of course: First Cycle (Undergraduate)
Type of course: Departmental Elective
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: Math 113
Professional practice: No
Purpose of the course: The aim of this course is to introduce the basics of coding theory. Morever, it will help students to understand the importance and applications of algebra in real life.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. List the basic notions of coding theory

    Contribution to Program Outcomes

    1. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Homework assignment
  2. Recognise finite fields, Reed-Solomon codes and use some decoding algorithms of these codes.

    Contribution to Program Outcomes

    1. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
    3. Being fluent in English to review the literature, present technical projects, and write journal papers.
    4. Using technology as an efficient tool to understand mathematics and apply it.
    5. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment
  3. Grab cyclic codes and some known bounds for the parameters of codes.

    Contribution to Program Outcomes

    1. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
    3. Using technology as an efficient tool to understand mathematics and apply it.

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
Week 1: Inntroduction to error correcting codes
Week 2: Linear codes
Week 3: Hamming codes
Week 4: Introduction to finite fields
Week 5: Roots of polynomials, primitive elements, field characteristic
Week 6: Some bounds for the parameters of codes
Week 7: Reed-Solomon codes and related codes
Week 8: Decoding algorithms, midterm
Week 9: Decoding Reed-Solomon codes by using Reed-Solomon codes
Week 10: Minimal polynomial, cyclotomic cosets
Week 11: Cyclic codes
Week 12: BCH codes
Week 13: BCH bound
Week 14: Some other bounds for the parameters of codes
Week 15*: -
Week 16*: Fianl exam
Textbooks and materials:
Recommended readings: R. M. Roth, Introduction to Coding Theory, Cambridge University Press, 2006
S. Ling, C. Xing, Coding Theory, A first course, Cambridge University Press, 2004
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 8 30
Other in-term studies: 0
Project: 0
Homework: 2,4,6,10,12 20
Quiz: 0
Final exam: 16 50
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 5 14
Practice, Recitation: 0 0
Homework: 2 5
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 10 1
Mid-term: 2 1
Personal studies for final exam: 10 1
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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