CO 331: Bonus Questions #1
Due date: February 15, 2015 (Friday), In Class
Instructions: There will be 5 bonus questions posted over the course of the semester. The total
grade can be used to replace the lowest assignment grade; if this does not improve yo

CO 331: Assignment #2
Due date: February 4, 2015 (Wednesday), In Class
1. The polynomial f (x) = x4 + 3x3 + 5 is irreducible over Z7 .
(a)
(b)
(c)
(d)
(e)
What is the characteristic of the field F = Z7 [x]/(f (x)?
Describe, in words, the elements of the f

CO 331: Assignment #3
Due date: March 4, 2015 (Wednesday)
1. [Note: for this question, you can only use results that we proved in class. In particular, you cannot
use the statement about the classification of perfect codes.]
(a) Does there exist a perfect

CO 331: Assignment #4
Due date: March 25, 2015 (Wednesday)
1. For i = 0, 1, let gi (x) be the generator polynomial for a binary (n, ki )-cyclic code Ci .
(a) Prove that g0 (x) | g1 (x) if and only if C1 C0 .
T
(b) Prove that C0 C1 is a cyclic code, and fi

CO 331: Bonus Questions #2
Due date: March 27, 2015 (Friday), In Class
[Note: the instructions have changed!]
Instructions: There will be bonus questions posted over the course of the semester. The total
grade can be used to replace the lowest assignment

CO 331: Assignment #5
Due date for #1 and #2: Monday, April 6, 2015, In-Class.
1. [10 marks] We will prove the following theorem in this question:
Theorem. Let C be an (n, k)-code over F with cyclic burst error correcting capability t. Let C be the
code o

CO 331: Assignment #1
Due date: January 21, 2015 (Wednesday), In Class
1. Consider the binary code C = cfw_c1 = 00000, c2 = 10110, c3 = 01011, c4 = 11101. Suppose that
P (c1 ) = 0.1, P (c2 ) = 0.2, P (c3 ) = 0.2, and P (c4 ) = 0.5, where P (ci ) denotes t