Homework 8
Due: Wednesday, April 23, 1998
Reading
Assignment.
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(a) MacWilliams &
Sloane, Chapters 3 & 9.
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(b) Peterson &
Weldon, Chapter 9
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(c) Berlekamp, Chapter
7
Problem
1. Let GF(24)
= GF(2)[X]/(X4+X+1) and let
a = X mod X4+X+1.
Let V = (g(x))
be the (15,5)
BCH code given by
g(X) = LCM( m1(X), m3(X),
m5(X) ),
where mi(X)
denotes the minimum polynomial of ai.
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(a) Find the maximum designed
distance of V.
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(b) Let r(X)
denote a received vector. If
r(a)= a5,
r(a3)
= a9,
and r(a5)
= a5,
then use the BCH decoding algorithm to find the most probable error pattern
e(X).
Note: If
you have not installed the symbol font on your web browser, then the above
alpha's will look like a's.
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Last Modified: April 16, 1998