Course Title: Coding Theory Course Code: MTH4241-3
Program: BSc. in Mathematics Department: Mathematics
College: Jamoum University College
Institution: Umm Al-Qura University
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Table of Contents
A. Course Identification ... 3
6. Mode of Instruction (mark all that apply) ... 3
B. Course Objectives and Learning Outcomes ... 3
1. Course Description ... 3
2. Course Main Objective ... 3
3. Course Learning Outcomes ... 3
C. Course Content ... 4
D. Teaching and Assessment ... 5
1. Alignment of Course Learning Outcomes with Teaching Strategies and Assessment Methods ... 5
2. Assessment Tasks for Students ... 5
E. Student Academic Counseling and Support ... 6
F. Learning Resources and Facilities ... 6
1.Learning Resources ... 6
2. Facilities Required ... 6
G. Course Quality Evaluation ... 6
H. Specification Approval Data ... 7
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A. Course Identification
1. Credit hours: 3 2. Course type
a. University College Department * Others
b. Required Elective *
3. Level/year at which this course is offered: 10 -12 level/4 year 4. Pre-requisites for this course (if any):
Rings and fields theory. 4044407-3 5. Co-requisites for this course (if any):
6. Mode of Instruction (mark all that apply)
No Mode of Instruction Contact Hours Percentage
1 Traditional classroom Four hours/week %100
2 Blended 0 0
3 E-learning 0 0
4 Distance learning 0 0
5 Other 0 0
7. Contact Hours (based on academic semester)
No Activity Contact Hours
1 Lecture 30
2 Laboratory/Studio 0
3 Tutorial 0
4 Others (specify) 0
Total 30
B. Course Objectives and Learning Outcomes
1. Course Description
Coding theory is a new subject in mathematical sciences. This course is an introductory course aiming to give students some basic knowledge in this science. This includes the concept and different method of describing codes as well as main theorems concerning the
main aim of coding theory.
2. Course Main Objective
This course will provide a common mathematical foundation for students in all of the
programs, drawing upon the full range of undergraduate courses in mathematics. In addition, it will permit students to build upon and share knowledge already acquired while pointing out areas in which additional study may be needed. In addition, it will develop the communication skills and understanding of the process of doing mathematics necessary for graduate-level study.
3. Course Learning Outcomes
CLOs Aligned
PLOs 1 Knowledge and Understanding: by the end of this course, the
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CLOs Aligned
PLOs student is expected to be able to
1.1 Identify statements, coding and related terminology.
1.2 Identify – weight and distance - Generating and check matrices.
1.3 Present basic concepts of linear codes.
1.4 State the main problem of coding theory
1.5 Describe some well-known types of codes such as BCH, Reed- Solomon-Muller codes.
1.6 Define the notion of group rings 1.7 Recognize linear codes as ideals
2 Skills: by the end of this course, the student is expected to be able to 2.1 Compare between codes (BCH, Reed Solomon and Reed Muller).
2.2 Use methods of solving problems for coding theory.
2.3 Apply algebraic structures on coding theory.
3 Values: by the end of this course, the student is expected to be able to
3.1 Prepare for success in disciplines which rely on coding theory and their types.
3.2 Interpret the main problem of coding theory.
3.3 Evaluate fundamental concepts of group rings for coding and zero divisors type codes.
3.4 Generalize mathematical models using linear codes.
C. Course Content
No List of Topics Contact
Hours 1
Introduction and motivation of coding theory:
Basic definitions – weight and distance - Generating and check matrices- 6 Encoding Error correcting codes; the main problem of coding theory.
2
Linear Codes:
Codes over finite fields – Equivalent codes - Cyclic linear Codes. 3
3
Bose–Chaudhuri–Hocquenghem (BCH Codes)
Finite fields – Minimal polynomials – Cyclic Hamming codes - Decoding 6 2 error correcting BCH code.
4
Reed-Solomon Codes:
3 Codes over Galois Fields with characteristic 2, Reed-Solomon codes.
5
Reed- Muller Codes:
3Constructing Reed-Muller codes – Decoding Reed-Muller codes.
6
Codes and Group Rings
6The notion of group rings and their structure, Linear codes as ideals in
5
group rings, Group rings as matrices, unit-type codes.
7
Zero divisors type codes:
3Zero divisors type codes.
Total 30
D. Teaching and Assessment
1. Alignment of Course Learning Outcomes with Teaching Strategies and Assessment Methods
Code Course Learning Outcomes Teaching Strategies Assessment Methods 1.0 Knowledge and Understanding
1.1 Identify statements, coding and related terminology.
Lecture and Tutorials Exams, quizzes 1.2 Identify – weight and distance -
Generating and check matrices.
Lecture and Tutorials Exams, quizzes 1.3 Present basic concepts of linear codes Lecture and Tutorials Exams, quizzes 1.4 State the main problem of coding
theory 1.5
Describe some well-known types of codes such as BCH, Reed-Solomon- Muller codes.
Lecture and Tutorials Exams, quizzes
1.6 Define the notion of group ring. Lecture and Tutorials Exams, quizzes 1.7 Recognize linear codes as ideals
2.0 Skills
2.1 Compare between codes (BCH, Reed Solomon and Reed Muller).
Lecture and Individual or group work
Exams, quizzes 2.2 Interpret the main problem of coding
theory.
Lecture and Individual or group work
Exams, quizzes 2.3 Apply algebraic structures on coding
theory.
Lecture and Individual or group work
Exams, quizzes
3.0 Values
3.1 Prepare for success in disciplines which rely on coding theory and their types.
Lecture and Individual or group work
Exams, quizzes
3.2 Interpret the main problem of coding theory.
Lecture and Individual or group work
Exams, quizzes 3.3 Evaluate fundamental concepts of
group rings for coding and zero divisors type codes.
Lecture and Individual or group work
Exams, quizzes
3.4 Generalize mathematical models using linear codes..
Lecture and Individual or group work
Exams, quizzes 2. Assessment Tasks for Students
# Assessment task* Week Due Percentage of Total
Assessment Score
1 Midterm exam 6th %25
2 Quizes and homeworks During semester %25
3 Final exam End of semester %50
*Assessment task (i.e., written test, oral test, oral presentation, group project, essay, etc.)
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E. Student Academic Counseling and Support
Arrangements for availability of faculty and teaching staff for individual student consultations and academic advice:
All faculty members are required to be in their offices outside teaching hours. Each member allocates at least 4 hours per week to give academic advice to students and to better explain the concepts seen during the lectures.
Students are required to complete the homework problems. Students are welcome to work together on homework. However, each student must turn in his or her own assignments, and no copying from another student's work is permitted. Deadline extensions for homework will not be given. Students are encouraged to discuss with professor about homework problems.
F. Learning Resources and Facilities
1.Learning ResourcesRequired Textbooks
1- Hoffman et. al., Coding Theory the essentials, Marcel Dekker, Inc.270 Madison Ave. New York. United states. ISBN:978-0- 8247-8611-3.
2- Introduction to the theory of Error-Correcting Codes.آNew York: WILEY, 1998. ISBN:047119047-9.
3- Steven Roman, Coding and Information Theory, Springer- Verlag 1992. Berlin. ISBN: 978-0-387-97812-3.
Essential References Materials Electronic Materials
Other Learning
Materials None
2. Facilities Required
Item Resources
Accommodation
(Classrooms, laboratories, demonstration rooms/labs, etc.)
Large classrooms that can accommodate more than 30 students
Technology Resources
(AV, data show, Smart Board, software, etc.)
Data Show, Smart Board Other Resources
(Specify, e.g. if specific laboratory equipment is required, list requirements or
attach a list)
None
G. Course Quality Evaluation
Evaluation
Areas/Issues Evaluators Evaluation Methods
Effectiveness of teaching and assessment
Students Direct
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Evaluation
Areas/Issues Evaluators Evaluation Methods
Quality of learning resources Students Direct Extent of achievement of
course learning outcomes
Faculty Member Direct
Evaluation areas (e.g., Effectiveness of teaching and assessment, Extent of achievement of course learning outcomes, Quality of learning resources, etc.)
Evaluators (Students, Faculty, Program Leaders, Peer Reviewer, Others (specify) Assessment Methods (Direct, Indirect)
H. Specification Approval Data
Council / Committee Council of the Mathematics Department
Reference No.
Date
