Homework 4
Due: Thursday, October 9, 1997
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Problem 1. 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).
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Problem 2. 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).
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Problem 3. Let
R be a
commutative ring with non-zero elements a
and b
such that
ab = 0
Prove that R
is not a field.
Last Modified: October 2, 1997