[ 0 0 2 2 0 2 ] [ 2 2 0 2 1 2 ] [ 1 1 2 0 2 2 ] [ 1 1 0 1 2 1 ]
·
Problem 2.
Let V be a binary linear code given by the
generator matrix
[ 101011 ] G = [ 011110 ] [ 000111 ]
o
a) Find a parity check
matrix H of V .
o
b) Construct a maximum
likelihood decoding table for V .
o
c) Use H to reduce the
maximum likelihood decoding table of b) to an error/syndrome table.
o
d) Demonstrate how your
error/syndrome table can be used to decode the received vector r = 111101.
o
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 11, 2001