This question concerns the field GF(256). The modulus is P(x) = x³ + x² + x³ + x + 1. For computing inverses in this field, you should use the table in the textbook. Please answer the following questions about arithmetic in this field. a) If p(x) = x² + x¹ + x² + x + 1, and g(x) = x² + x³ + x² + x³ + x² + x + 1, what is p(x)/q(x)? b) If p(x) = x² + x³ + x² + x + 1, and q(x) = x² + x4 + x² + 1, what is p(x)/q(x)?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 87E
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This question concerns the field GF(256). The modulus is P(x) = x³ + x² + x³ + x + 1.
For computing inverses in this field, you should use the table in the textbook.
Please answer the following questions about arithmetic in this field.
a) If p(x) = x² + x¹ + x² + x + 1, and g(x) = x² + x³ + x² + x³ + x² + x + 1, what is p(x)/q(x)?
b) If p(x) = x² + x³ + x² + x + 1, and q(x) = x² + x4 + x² + 1, what is p(x)/q(x)?
Transcribed Image Text:This question concerns the field GF(256). The modulus is P(x) = x³ + x² + x³ + x + 1. For computing inverses in this field, you should use the table in the textbook. Please answer the following questions about arithmetic in this field. a) If p(x) = x² + x¹ + x² + x + 1, and g(x) = x² + x³ + x² + x³ + x² + x + 1, what is p(x)/q(x)? b) If p(x) = x² + x³ + x² + x + 1, and q(x) = x² + x4 + x² + 1, what is p(x)/q(x)?
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