MATH747 ASSIGNMENT 1
FALL 2014
Due Friday September 14 in class.
(1) Give a real world example where error detection or error correction is used. State
which coding scheme is used in the example and give as many of the parameters
which we have discussed i
MATH747 ASSIGNMENT 4
FALL 2014
The following questions are optional questions. They do not need to be handed in and
will not be graded if they are handed in
Vanstone and van Oorschot section 3.9 # 18.
Vanstone and van Oorschot section 4.4 # 3 parts a an
MATH747 ASSIGNMENT 5
FALL 2014
The following questions are optional questions. They do not need to be handed in and
will not be graded if they are handed in
Vanstone and van Oorschot section 4.4 # 11.
Vanstone and van Oorschot section 5.10 # 1, 7
The fo
MATH747 ASSIGNMENT 2
FALL 2014
Due Friday September 21 in class.
(1) Let F = Z3 /(1 + x2 ) and F = Z3 /(2 + x + x2 ).
(a) Give the multiplication table for F
(b) Give an explicit isomorphism between F and F (for comparison the multiplication table for F i
MATH747 ASSIGNMENT 1 SOLUTIONS
FALL 2014
(1) Many answers possible; nding all the parameters wasnt necessary, better to have an
interesting example.
6
3
(2) (a) The rate is 32 = 16 .
12
1
(b) The rate is 24 = 2 .
(3) (a) Let the codewords be cfw_c1 , c2 ,
MATH747 ASSIGNMENT 3
FALL 2014
The following questions are optional questions. They do not need to be handed in and
will not be graded if they are handed in
Vanstone and van Oorschot section 3.9 # 13, 21
Vanstone and van Oorschot section 3.9 # 26. What
SIMON FRASER UNIVERSITY
DEPARTMENT OF MATHEMATICS
Midterm
Math 747 Fall 2014
Instructor: Dr. Yeats
October 14, 2014
Name:
(please print)
family name
SFU email:
given name
@sfu.ca
SFU-email
Signature:
Instructions:
(1) Fill in your information above.
(2) S
MATH747 ASSIGNMENT 8 SOLUTIONS
FALL 2014
hand in questions
(1) #8 First observe the the cyclotomic cosets are
C0 = cfw_0
C1 = cfw_1, 2, 4, 8
C3 = cfw_3, 6, 12, 9
C5 = cfw_5, 10
C7 = cfw_7, 14, 13, 11
and appendix D tells us the corresponding minimal polyn
MATH747 ASSIGNMENT 5 SOLUTIONS
FALL 2014
Not to hand in questions
Let c be a row of G. Then c c = 0 since c has weight divisible by 4. Along with the
given fact that the rows of G are pairwise orthogonal we get GGT = 0 and so C is
self-orthogonal.
Take a
MATH747 ASSIGNMENT 8
FALL 2014
The following questions are to be handed in. They are due Friday November 30 in
class.
(1) Vanstone and van Oorschot section 6.6 # 8, 20, 30
(2) Summarize in a few lines the proof that the algorithm for decoding BCH codes wo
MATH747 ASSIGNMENT 7
FALL 2014
Optional question
(1) (5.10 #42)
(a) Let D be the Hamming code we began with. Note that d(C) d(D) = 3
so C can correct all single errors. Also let v(i ) denote the binary r-tuple
corresponding to i .
First I claim that a par
MATH747 ASSIGNMENT 3
FALL 2014
The not to hand in questions
#13 (a) No column of H is 0 and no column in a multiple of another, while column 1
plus column 2 equals column 3, so the distance of this code is 3 and thus e = 1.
n = 4 and we are over Z3 and so
MATH747 ASSIGNMENT 7
FALL 2014
The following questions are optional questions. They do not need to be handed in and
will not be graded if they are handed in
Vanstone and van Oorschot section 5.10 # 42
Vanstone and van Oorschot section 6.6 # 9
The follow