Homework 2
Due: Monday, February 16, 1998
- Reading Assignment
- Peterson & Weldon, Error-Correcting Codes, Chap. 3, Sections 3.1, 3.3, 3.4
- MacWilliams & Sloane, The Theory of Error-Correcting Codes, Chap. 1, Sections 1 to 5
- Pless, Introduction to Error-Correcting Codes, Chap 1
- Berlekamp, Algebraic Coding Theory, Chap 1, Sections 1.1, 1.2
-
Problem 1.
Let V be a binary linear code given
by the generator matrix
[ 101011 ]
G = [ 011110 ]
[ 000111 ]
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a) Find a parity check matrix H of V .
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b) Construct a maximum likelihood decoding table
for V .
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c) Use H to reduce the maximum likelihood decoding
table of b) to an error/syndrome table.
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d) Demonstrate how your error/syndrome table can
be used to decode the received vector r = 111101.
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e) Use the generator matrix to create a list of
all code vectors of V. Then use this list to determine the minimum distance
of V.
Last Modified: February 10, 1998