Syllabus for Math 4452 (Algebraic Coding Theory) Spring 2022

TuTh 2-3:15 pm, Maury 113.

Main text (required): Coding Theory: A First Course by San Ling and Chaoping Xing, first edition, ISBN 9780521529235.

Other recommended sources:

Course outline and prerequisites

This course is an introduction to the theory of error-correcting codes, that is, codes designed to provide reliable transmission of information in the presence of noise. The topics will include a general theory of linear codes, a detailed discussion of some particular classes of codes (e.g. Hamming codes, Golay code, Reed-Solomon codes), and the associated encoding and decoding algorithms. Specific (real life) applications of codes will also be briefly discussed. A few lectures will be devoted to developing necessary algebraic background for the course, mainly basic theory of finite fields. The precise selection of topics will depend on the interests of the students taking the course and may not be determined until a few weeks after the start of the semester.

The prerequisites for Math 4452 are Math 3351 Elementary Linear Algebra and Math 3354 Survey of Algebra. In addition, a substantial prior exposure to proof-based mathematics will be expected. The proofs will often use elementary combinatorial arguments, so a prior course in discrete mathematics will likely be helpful, but is by no means expected or required.

Evaluation

The course grade will be based on homework, two midterms and the final, with weights distributed as follows:

Exams

The format of the exams (in-class or take-home) has not been finalized at this point and will be announced at a later point. The midterm dates given below are tentative and may be changed later. The date and time of the final exam is determined by the registrar and cannot be changed (in case the exam is held in class).

Make-up policy for exams

Homework

Collaboration policy on homework.

Announcements

Major announcements will be made in class and also posted on the course webpage. Some other announcements may only be made by e-mail, so check your e-mail account regularly.

Add/drop/withdrawal dates:

SDAC

All students with special needs requiring accommodations should present the appropriate paperwork from the Student Disability Access Center (SDAC). It is the student's responsibility to present this paperwork in a timely fashion and follow up with the instructor about the accommodations being offered. Accommodations for test-taking (e.g., extended time) should be arranged at least 5 business days before an exam.