Error Control Coding Asssignment 4
Due 11:00 am Friday 3 June 2011
Value in brackets indicates marks for each question. Total value of marks is 20. This assignment
counts towards 12.5% of the total assessment.
Question 1 (6): A (15,11) cyclic code has the generator polynomial
g
(
X
) = 1+
X
+
X
4
.
(a) Show that this code does not have any code words of weight 1 or 2.
(b) Show that there are at least 30 code words of weight 3. (Hint: use
g
(
X
) and
g
(
X
)
2
.)
(c) Devise a systematic encoder for this code.
(d) Devise a Meggitt decoder for this code.
Question 2 (4): We have the generator polynomial
g
(
X
)
+
1
)
X
2
)
X
4
)
X
6
)
X
7
)
X
10
(a) Show that
g
(
X
) generates a (21,11) cycle code.
(b) Devise a syndrome computation circuit for this code.
(b) Let
r
(
X
)
+
1
)
X
5
)
X
17
be a received polynomial. Compute the syndrome of
r
(
X
). Display
the contents of the syndrome register after each digit of
r
has been shifted into the syndrome com
putation circuit.
Question 3 (4): Let
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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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