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University of Victoria
Department of Electrical and Computer Engineering
ELEC 511
Error Control Coding Techniques in Communications
2010
Assignment 2
1. Consider the set of binary vectors of length 6.
a) Is it possible to Fnd eight vectors with minimum Hamming distance 3?
b) Is it possible to Fnd nine vectors with minimum Hamming distance 3?
2. Construct a standard array for the ternary Hamming [4,2,3] code.
3. Let
C
be a binary linear [
n, k, d
] code with generator matrix
G
. We may assume that
the Frst row of
G
has the form 1
···
10
···
0, so that
G
=
b
1
···
1 0
···
0
G
1
G
2
B
.
Let
d
2
be the minimum distance of the [
n

d, k

1] code with generator matrix
G
2
.
Show that
d
2
≥
d/
2.
4. If a binary linear code
C
has parity check matrix
H
, what is the parity check matrix of
the extended code
C
′
obtained by adding an overall parity check to each codeword.
5. Devise a single error correcting code for the 7bit ASCII character set.
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This note was uploaded on 10/16/2011 for the course ELECTRICAL EE251202 taught by Professor Rejaei during the Spring '10 term at Sharif University of Technology.
 Spring '10
 Rejaei
 Electromagnet

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