Homework 8
Due: Tuesday, November 18, 1997
Problem 1.
Factor( x31 + 1 ) mod 2 ;
Problem 2. Let
V denote
the cyclic code of length 15
in R15 given by the generator polynomial:
g(x) = x8 + x4 + x2
+ x + 1.
-
(a) Use g(x)
to compute the generator matrix G
of V.
What is the dimension of V
?
-
(b) Compute
h+(x)
of V.
-
(c) Use h+(x)
to compute a generator matrix H+
of V+.
-
(d) From h+(x),
compute the parity check polynomial h(x)
of V.
-
(e) Use the parity
check polynomial h(x)
computed in (d)
to compute the parity check matrix H
of V.
-
Last Modified: November 13, 1997