Recall the following table, which shows that is a primitive element of the field GF(16) Z₂[x]/(x¹+x+1). = power of a polynomial power of a 0 polynomial x² +1 28 x x³ + x 22 +x+1 x3 x3 x³ + x² + x x+1 +x²+x+1 x² + x 76 x³ + x² x³ + x² +1 x3+1 x7 x³ + x + 1 x15 1 Find the minimal annihilating polynomials over Z₂ for a = x5 and b = x7. x5 x x2 x10 all x12 x13 x14 2²
Recall the following table, which shows that is a primitive element of the field GF(16) Z₂[x]/(x¹+x+1). = power of a polynomial power of a 0 polynomial x² +1 28 x x³ + x 22 +x+1 x3 x3 x³ + x² + x x+1 +x²+x+1 x² + x 76 x³ + x² x³ + x² +1 x3+1 x7 x³ + x + 1 x15 1 Find the minimal annihilating polynomials over Z₂ for a = x5 and b = x7. x5 x x2 x10 all x12 x13 x14 2²
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Recall the following table, which shows that x is a primitive element of the field GF(16)
Z₂[x]/(x¹ + x + 1).
=
power of polynomial
power of x
0
polynomial
x² +1
x8
X
X
x³ + x
x²
x²
x² + x + 1
x3
x³ + x² + x
x+1
+ x² + x + 1
x² + x
x³ + x²
x³ + x² +1
x³ +1
x7
x³ + x + 1
x15
1
Find the minimal annihilating polynomials over Z₂ for a = x5 and b = x7.
x³
25
2.6
x9
x10
all
x12
x13
x14
x3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a8575b3-efc7-4bb3-9311-229ad0932cc0%2Ff356a65a-f7d2-4f7f-bd18-2f47a922b134%2F56u2fc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Recall the following table, which shows that x is a primitive element of the field GF(16)
Z₂[x]/(x¹ + x + 1).
=
power of polynomial
power of x
0
polynomial
x² +1
x8
X
X
x³ + x
x²
x²
x² + x + 1
x3
x³ + x² + x
x+1
+ x² + x + 1
x² + x
x³ + x²
x³ + x² +1
x³ +1
x7
x³ + x + 1
x15
1
Find the minimal annihilating polynomials over Z₂ for a = x5 and b = x7.
x³
25
2.6
x9
x10
all
x12
x13
x14
x3
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