Math 342
Algebra and Coding Theory


Information for Final Exam: Will be held APR 18 2016 07:00 PM in BUCH A104. The final exam will cover the entire course. A practice final is posted below. The undergraduate tab on the Math Department website contains some past final exams.

Review Session: Thursday, April 14, 7:30PM - 9:00PM, Math 105

Office hours for week of April 11: Wednesday, Thursday, Friday: 2:30 - 4:00

Solutions to Practice Final

Practice Final

Midterm 2 and solutions

Solutions to Practice Midterm 2

Practice Midterm 2

No regular office hours for week of Feb. 22. Office hours by appointment only on Feb. 25 and 26. Prof. Lior Silberman will teach class on Feb. 23 and return midterm papers. Prof. Marcus will be back on Feb. 25.

Midterm 1 and Solutions

Midterm 1, Thursday, Feb. 11: Will cover material in Lectures 1-8 plus material in Lectures 9-10, pertaining to groups. Fields and rings will not be covered. But Z_m as a group with addition mod m will be covered. Much of the material is contained in Chapters 1 and 2 of the text. Midterm is closed book. No notes, calculators or books.

Solutions to Practice Midterm 1

Practice Midterm 1

Office hours for week of Feb 8: Tuesday: 1:30 - 3:30, Wednesday: 1:00 - 3:00

Questions regarding registration for this class should be addressed to the Mathematics Department office staff Room 121 Mathematics Building.

Homework assignments will be posted bi-weekly below. First homework will be due on Thursday, January 21. For information on homework policy, see below.

Midterm 1, Thursday, Feb. 11; Midterm 2: Thursday, March 17
For information on midterm policy, see below..

Table of bounds for best codes

Handout: Two finite rings with 4 elements

Handout: Standard Array and Syndrome Table for the code C_3

Proof of Euclidean Algorithm and Bezout Theorem

Lecture Notes, April 5 and 7

Lecture Notes, March 29 and 31

Lecture Notes, March 22 and 24

Lecture Notes, March 15

Lecture Notes, March 8, 10

Lecture Notes, March 1,3

Lecture Notes, Feb 23, 25

Lecture Notes, Feb 9

Lecture Notes, Feb 2, 4

Lecture Notes, Jan 26, 28

Lecture Notes, Jan 19, 21

Lecture Notes, Jan 12, 14

Lecture Notes, Jan 5,7

British Columbia law requires the use of a helmet while riding a bicycle.

Instructor Information

Instructor: Brian Marcus
Email : marcus[at]math[dot]ubc[dot]ca
Office: Math Building, Room 218 (604)
Office Hours:  Tuesday and Wednesday 1:30- 2:50 and by appointment
Phone: 822-3262

Course Information

Section: 201
Class time:  TuTh 9:30
Class location:  LSK 460

Course web page: will be updated throughout the term.

Text:  A First Course in Coding Theory, by Raymond Hill, 1986, reprinted 2009
Course Description :
The course is an introduction to abstract algebra and error-correcting codes. Both proof and algorithmic techniques will be emphasized. Topics will include coding and decoding schemes, finite fields, vector spaces over finite fields, linear codes, syndrome decoding, Hamming codes, coding bounds, BCH codes and Reed-Solomon codes.


Your course mark will be based on homework, the midterms and the final exam. The final course mark will be roughly determined by:

Homework (15%) + Midterms (35%) + Final Exam (50%)

Missed Exam Policy: Please make sure you do not make travel plans, work plans, etc., without regard to the examination schedule in this class. There will be no make-up or alternate exams.

If you miss a midterm, your score will be recorded as 0, unless you have a serious documented reason (an illness, a death in the family, etc.), in which case you should discuss your circumstances with the instructor as soon as possible, and in advance of the test.

Missed finals are not handled by the instructor or the Mathematics Department. Students with legitimate reasons for missing the final exam should request a "Standing Deferred" status through their Faculty.

Academic Integrity: The Mathematics Department strictly enforces UBC's Academic Integrity Code.

Homework Assignments

Homework will be assigned bi-weekly and collected in class on Thursdays. Late homework will NOT be accepted. The lowest homework grade will be dropped. Students are allowed to consult one another concerning homework problems, but solutions submitted for credit must be written by the student in his or her own words. Copying solutions from another student, from the web or from any other source, and turning them in as your own is a violation of the Academic Code.

Resources for help:

Come to office hours or Math Learning Centre (MLC) in LSK 301 and 302.
Students with Disabilities

Please see the instructor as soon as possible if you need any special accommodations.

Homework #1 due Thursday, January 21 (problem 4 corrected at 2PM on Jan. 16)


Homework #2 due Thursday, February 4 (corrected Jan. 31, 12 PM)


Homework #3 due Thursday, March 3


Homework #4 due Thursday, March 10


Homework #5 due Thursday, March 24


Homework #6 due Friday, April 8, 5PM in my office