CO 331: Assignment 2: Solutions
1. (a) q = 55 = 3125.
(b) The (equivalence classes of) polynomials in Z5 [x] of degree less than 5.
i. 2x4 + 2x3 + x + 4.
ii. 3x4 + 2x3 + x (expand and simplify using the identity x5 = x + 3.)
iii. Note that a5
C&O 331: Midterm Test
Duration: 1 hour 15 minutes
March 2, 2017
Total marks: 60
1. [15 marks] Let C be a binary (n, k)-code.
(a) How many codewords are in C? (Explain)
There are 2k codewords in C. This is because C is a k-dimensional vector spa
CO 331: Assignment 3 Solutions
1. (a) Since H is a 2 10 matrix of rank 2, C is a (10, 8) code. Since none of the columns of H are zero,
and no column is a multiple of another column, it follows that C has distance at least 3. Finally,
since C has at least
CO 331: Assignment 5
Due date: Monday 3 April.
1. (a) Let C be the binary cyclic (7, 3)-code with generator polynomial g(x) = 1 + x2 + x3 + x4 . Show
that C is a 2-cyclic burst error correcting code.
(b) Let C be the binary cyclic (14, 6)-code with genera
CO 331: Assignment 4
Due date: March 16, 2017, in class.
1. Decode each of the following received words using the decoding scheme for C24 (the extended binary
(a) r1 = (0000 0000 0011 1111 1101 1001).
(b) r2 = (0011 1000 0000 0100 1100 1110).
CO 331: Assignment 3
Due date: Thursday Feb 16, 2017, beginning of class.
Please note that assignments are not weighted equally. Each problem on each assignment is worth 10 marks
(unless otherwise noted.) The total marks received on assignments will be ad