Department of Mathematics
University of British Columbia
MATH 342 SAMPLE Midterm 1 SOLUTIONS
Family Name:
Initials:
I.D. Number:
Problem
Signature:
Mark
Out of
1
20
2
20
3
15
4
15
5
15
6
15
Total
100
CALCULATORS, NOTES OR BOOKS ARE NOT PERMITTED.
THERE AR
Lecture 1:
All administrative information on course website:
http:/www.math.ubc.ca/marcus/Math342
(or link through Math Dept website)
Introduction to abstract algebra through coding theory.
Abstract algebra: theory developed for solving polynomial equatio
Department of Mathematics
University of British Columbia
MATH 342 Midterm 1
February 6, 2014 9:30 AM - 10:50 AM
Family Name:
Initials:
I.D. Number:
Problem
Signature:
Mark
Out of
1
20
2
20
3
20
4
20
5
20
Total
100
CALCULATORS, NOTES OR BOOKS ARE NOT PERMI
Math 342
Homework 1.1
15 January 2015
This is an updated version of Homework 1, with clarifying material added to questions 1 & 3.
1 For each of the following codes, explain:
How many errors it can detect, if it is used to detect errors.
How many errors
MATH 342 MIDTERM
9:30am, 5th February, 2015
There are 5 questions, they carry equal weight. Answer all questions. This exam should be 10 pages
long, and conclude with the symbol .oOo. Please check that this is the case.
Show all your work.
No notes, calcu
Math 342
Homework 2
27 January 2015
1. Read the supplementary notes on equivalences of codes.
2. In each of the following cases, either prove that the given codes are not equivalent or describe an
equivalence between then (to demonstrate an equivalence, i
Math 342
Homework 3
26 February 2015
1. Let n 1 be an integer. Suppose cfw_G 1 , . . . ,G n is a nite set of groups. Dene the set G = G 1 G 2
G n of ordered n-tuples (g 1 , g 2 , . . . , g n ) where g i G i . Show that the operation : G G G
given by
(g
MATH 342 MIDTERM 2
9:30am, 12th March, 2015
There are 5 questions, they carry equal weight. Answer all questions. This exam should
be 8 pages long, and conclude with the symbol .oOo. Please check that this is the case.
Show all your work.
No notes, calcul
Math 342
Homework 5
26 March 2015
1. Let F = Z/(2Z). Consider the linear code, C , over F described by the parity check matrix
0
1
P =
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
.
0
1
Throughout this question, P will be used to calculate syndromes: s
Math 342
Homework 4
5 March 2015
1. Consider the binary linear code (i.e., a linear code over the eld F = Z/2Z) with generator matrix
1
G = 0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
(a) Find a generator matrix G in standard form for an equivalent code.
(b)
MATH 342 SAMPLE MIDTERM 2
9:30am, 12th March, 2015
There are 5 questions, they carry equal weight. Answer all questions. This exam should
be 10 pages long, and conclude with the symbol .oOo. Please check that this is the
case.
Show all your work.
No notes
MATH 342 PRACTICE MIDTERM
9:30am, 5th February, 2015
There are 5 questions, they carry equal weight. Answer all questions. This exam should be 6 pages
long, and conclude with the symbol .oOo. Please check that this is the case.
Show all your work.
No note
Math 342, Fall Term 2011
Final Exam
December 9th ,2011
Student number:
LAST name:
First name:
Signature:
Instructions
Do not turn this page over. You will have 150 minutes for the exam.
You may not use books, notes or electronic devices of any kind.
So
Lecture 15:
Recall defn. of wt(x) and fact: d(x, y) = wt(x y).
Defn: for a linear code C, the weight of C is
wt(C) =
min
wt(x)
xC, x=0
Proposition: For a linear code C, d(C) = wt(C).
Proof: Let x, y C, x = y, that achieve d(C), i.e., d(C) =
d(x, y). Then
Final Exam
Math 342 Section 101 December 11th 2010
Name
Student Number
Signature
The exam is 150 minutes long and worth a total of 100 points. No books, notes or calculators
may be used. Show all of your work and justify your answers carefully. You will b
Lecture 19:
Midterm, Review Session, Info sheet (review HW4,5,6,7), Lecture
notes, Sample Midterm
Comments from TA:
Todays material will not be on midterm.
Recall defn. of characteristic and fact: characteristic of a nite
eld is prime.
Prop: if F is a nit
Department of Mathematics
University of British Columbia
MATH 342 Midterm 2
March 20, 2014 9:30 AM - 10:50 AM
SOLUTIONS
Family Name:
Initials:
I.D. Number:
Problem
Signature:
Mark
Out of
1
20
2
20
3
20
4
20
5
20
Total
100
CALCULATORS, NOTES OR BOOKS ARE N
Department of Mathematics
University of British Columbia
MATH 342 SAMPLE Midterm 2
9:30 - 10:50
SOLUTIONS
Family Name:
Initials:
I.D. Number:
Problem
Signature:
Mark
Out of
1
20
2
20
3
20
4
20
5
20
Total
100
CALCULATORS, NOTES OR BOOKS ARE NOT PERMITTED.
Department of Mathematics
University of British Columbia
MATH 342 SAMPLE Midterm 1
Family Name:
Initials:
I.D. Number:
Problem
Signature:
Mark
Out of
1
20
2
20
3
15
4
15
5
15
6
15
Total
100
CALCULATORS, NOTES OR BOOKS ARE NOT PERMITTED.
THERE ARE 6 PROBLE
Lecture 23:
Recall: Last time we proved:
Theorem: Let F be be a eld. The quotient ring F [x]/f (x) is a
eld i f (x) is irreducible.
This explained why F2[x]/(x2 + x + 1) is a eld but F2[x]/(x2 + 1)
is not.
Theorem 3.3.3: For every prime p and positive int
Department of Mathematics
University of British Columbia
MATH 342 SAMPLE Midterm 2
9:30 - 10:50
Family Name:
Initials:
I.D. Number:
Problem
Signature:
Mark
Out of
1
20
2
20
3
20
4
20
5
20
Total
100
CALCULATORS, NOTES OR BOOKS ARE NOT PERMITTED.
THERE ARE
Department of Mathematics, University of British Columbia
MATH 342, Section 201
Final Exam - Alternate Sitting
Closed book. Calculators, laptops, notes, cheat sheets, etc. are NOT allowed.
THIS EXAM CONSISTS OF 8 NUMBERED PROBLEMS, EACH WORTH THE
SAME VAL
Department of Mathematics, University of British Columbia
MATH 342, Section 201
Final Exam
Closed book. Calculators, laptops, notes, cheat sheets, etc. are NOT allowed.
THIS EXAM CONSISTS OF 8 NUMBERED PROBLEMS, EACH WORTH THE
SAME VALUE.
JUSTIFY ALL OF Y
Lecture 9:
Reminder of Review Session, Oce Hours for this week (no oce
hours on Tuesday, Feb. 11), Midterm 1
Pointer to website info.
Review end of proof of: Theorem 3.1.9: Zm is a eld i m is prime
(dierent from proof in text).
If: Assume m is prime.
Clai
Department of Mathematics, University of British Columbia
MATH 342, Section 201
Final Exam
Closed book. Calculators, laptops, notes, cheat sheets, etc. are NOT allowed.
Time: 3:30PM - 6:00PM
Date: April 28, 2008.
Name:
Student No.
Signature:
Problem
1
2
3
Lecture 17:
Recall:
Theorem: Let C be a linear code with parity check matrix H.
Then d(C) is the minimum size of a set of linearly dependent columns.
Note: The parity check matrix of a linear code is not unique, yet
you get the same d(C) for all parity ch
Mathematics 342, Coding Theory, Practice Final Exam
Thursday, 19th April, 2014. 12pm2:30pm.
There are eight (8) questions, they carry equal weight. Answer all questions. Some questions take up
two page. The exam should be 10 pages long, and conclude with