Intro Coding Theory - Spring 2005

Instructor: Markus Schmidmeier
Department of Mathematical Sciences
Charles E. Schmidt College of Science
Introduction to Coding Theory

Spring 2005

Welcome to my course Introduction to Coding Theory (MAD 4605/MAT 5932)! We meet Tuesday and Thursday, 9:30 - 10:50 a.m. in Physical Sciences PS 109. Pre-requisite for this course is Matrix Theory (MAS 2103).

Textbook

We use the textbook by San Ling and Chaoping Xing, Coding Theory - A First Course, Cambridge University Press, 2004, ISBN 0-521-52923-9.

Topics

Error Detection and Correction (Chapter 2) Practise encoding and decoding using some basic codes; get used to the setup in coding theory; work with concepts like binary symmetric channel, maximum likelihood decoding, distance of codewords.

Some Mathematics (Chapter 3) Recall operations in the polynomial ring; construct finite fields and their extensions; perform computations in finite fields.

Linear Codes (Chapter 4) Use generator and parity check matrices for encoding and decoding; compute syndromes and coset leaders.

Bounds in Coding Theory (Chapter 5) Understand the main coding theory problem; compute minimum distance and covering radius for a given code; determine upper and lower bounds for the number of code words; design Hamming codes for given parameters; specify relations between further bounds.

Cyclic Codes (Chapter 7) Construct cyclic codes for given generator polynomials; determine all possible cylic codes of certain types; decode using parity check polynomials; design codes with burst error correction capability.

BCH and Reed-Solomon codes (Chapter 8) Recall operations in field extensions of finite fields; design BCH and Reed-Solomon codes for given parameters.

Further Topics as time permits (Chapter 9) Construct Goppa codes; decode Reed-Solomon codes.

Credit

Homework Problems: Some homework problems will be assigned every week; many quiz and exam problems will be taken from the homeworks. Here is a list of current homework problems.

Quizzes: There'll be a quiz every Thursday. All quizzes determine 1/3 of the grade.

Midterm Exam: The midterm exam will count for 1/4 of the grade.
It is scheduled for Thursday, March 24, during class time.

Final Exam: The final exam appears to be scheduled for Thursday, May 5, 7:45 - 10:15 a.m. It will count for 5/12 of the grade.

For your Calendar

Please see the academic calendar http://www.fau.edu/registrar/docs/acadcal0405.pdf for withdrawal and drop dates.

Contact Me

Office hours: MW 8-9 p.m., TR 11-12 a.m. in SE 278

Telephone: 561-297-0275

E-mail: markus@math.fau.edu

On the Web: http://www.math.fau.edu/schmidme/

Last modified: , by Markus Schmidmeier

Error Detection and Correction (Chapter 2)	Practise encoding and decoding using some basic codes; get used to the setup in coding theory; work with concepts like binary symmetric channel, maximum likelihood decoding, distance of codewords.
Some Mathematics (Chapter 3)	Recall operations in the polynomial ring; construct finite fields and their extensions; perform computations in finite fields.
Linear Codes (Chapter 4)	Use generator and parity check matrices for encoding and decoding; compute syndromes and coset leaders.
Bounds in Coding Theory (Chapter 5)	Understand the main coding theory problem; compute minimum distance and covering radius for a given code; determine upper and lower bounds for the number of code words; design Hamming codes for given parameters; specify relations between further bounds.
Cyclic Codes (Chapter 7)	Construct cyclic codes for given generator polynomials; determine all possible cylic codes of certain types; decode using parity check polynomials; design codes with burst error correction capability.
BCH and Reed-Solomon codes (Chapter 8)	Recall operations in field extensions of finite fields; design BCH and Reed-Solomon codes for given parameters.
Further Topics as time permits (Chapter 9)	Construct Goppa codes; decode Reed-Solomon codes.

Office hours:	MW 8-9 p.m., TR 11-12 a.m. in SE 278
Telephone:	561-297-0275
E-mail:	markus@math.fau.edu
On the Web:	http://www.math.fau.edu/schmidme/