Homework 3
Due: Monday, February 23, 1998
Reference
numbers refer to the numbered references given in the syllabus.
-
Problem 1.
Devise a procedure for correcting double erasures
for
the Hamming
[2m-1,
2m-1-m, 3] code.
Reading Assignment:
-
Peterson(Ref#7), Chap 5, Sect. 5.1-5.3
-
MacWilliams(Ref#6), Chap 1, Sect. 7-9
-
Berlekamp(Ref#1), Chap 1, Sect. 1.1-1.3
-
Problem 2.
Let V
be the binary [15,11,3]
Hamming code.
a) Compute the weight enumerator
of the null space of V.
b) Then use the MacWilliams identity
to compute the weight enumerator of V
.
Reading Assignment
-
Peterson(Ref#7), Chap 3, Sect. 3.8
-
MacWilliams(Ref#6), Chap 5, Sect. 1-2
-
Problem 3.
The polynomial
p(x) = x6 + x5 + 1
is primitive (hence, irreducible) over GF(2).
Use p(x) to
construct a log/antilog table for GF(26).
Reading Assignment
-
Peterson(Ref#7), Chap 6
-
MacWilliams(Ref#6), Chap 4, Sect. 1-6
-
Pless(Ref#8), Chap 4
-
Problem 4.
The polynomial p(x)
= x2 + x + 2 is primitive
(hence, irreducible) over GF(3).
Use p(x) to construct a
log/antilog table for
GF(32).
Reading Assignment
-
Same reading assigment as Problem 3 above.
Last Modified: February 18, 1998