# 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.
• 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 .
• 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).

• 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).