Syllabus for Math 4452 (Algebraic Coding Theory) Spring 2022
TuTh 2-3:15 pm, Maury 113.
- Instructor: Mikhail Ershov
- Office: Kerchof 302
- e-mail: ershov at virginia dot edu
- Regular office hours: Thu 6-7:30 and Fri 5-6:30
- Course webpage: https://m-ershov.github.io/4452_Spring2022/
Main text (required): Coding Theory: A First Course by San Ling and Chaoping Xing, first edition, ISBN 9780521529235.
Other recommended sources:
- Lecture notes by Prof. Jonathan Hall, based on an advanced undergraduate/graduate course at Michigan State University
- Lecture notes by Prof. Yehuda Lindell, based on a graduate course for computer science students at Bar-Ilan University
- A First Course in Coding Theory by Raymond Hill, ISBN 9780198538035
- Coding Theory and Cryptography: The Essentials by D.C. Hankerson, Gary Hoffman, D.A. Leonard, Charles C. Lindner, K.T. Phelps, C.A. Rodger and J.R. Wall, ISBN 9780824704650
- Introduction to Coding Theory by Ron Roth, ISBN 9780521845045
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:
- homework: 30%
- midterms: 20% each
- final: 30%
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).
- First midterm exam: Thu, Mar 3rd
- Second midterm exam: Thu, Apr 14th
- Final exam: Thu, May 12th, 9am-12pm
Make-up policy for exams
- Make-ups or extensions (for take-home exams) will be given only under extreme circumstances (such as
serious illness). Except for emergencies, you must obtain my permission
for a make-up (resp. extension) before the exam (resp. due date).
- If you miss an in-class exam or fail to submit a take-home exam
by the due date without a compelling reason, you will
be assigned the score of 0 on that exam.
- University regulations specifically prohibit early make-ups.
Homework
- Homework will be assigned weekly
- No late homework will be accepted. However, two lowest
homework scores will be dropped.
- GRADING: it will not be possible to grade all homework problems. In each assignment 3-4 selected (but not announced in advance) problems will be graded for credit.
Collaboration policy on homework.
- On homework: you are welcome (and even encouraged)
to work on homework together, but you must write
up solutions independently, in your own words. In particular,
you should not be consulting others during the process of
writing down your solution.
- On take-home exams: you MAY NOT discuss problems with other people
or use any resources (including web) except for the class textbook and your
class notes. You may ask me questions about the exam problems, but normally
I will only provide very brief hints.
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:
- Wednesday, February 2 -- Last day to add a class, select the AU (audit) option or change to or from "Credit/No Credit" Option
- Thursday, February 3 -- Last day to drop a class
- Wednesday, March 23 -- Last day to withdraw from a course
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.