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Question 0.6. Let Alice send Bob a message using a linear code V, and suppose e of the bits are garbled. Show that, if e

Question 0.6. Let Alice send Bob a message using a linear code V, and suppose e of the bits are garbled. Show that, if e

Algebra & Trigonometry with Analytic Geometry
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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Let p be a prime number. For example, p could be 2,3,5,7, etc. We define a field Fp consisting of the elements {0, 1, 2, . . . , p − 1} with operations +, −, ×, ÷ considered only up to remainder when we divide by p. For example,in F5,2+4 = 6≡ 1,2−4 = −2 ≡ 3,and2×4 = 8 ≡3. SinceF5, 4 × 3 = 12 ≡ 2 (you can check that the multiplication of 4 with any other element in F5 is never 2), we say that 2 ÷ 4 ≡ 3 in F5.

Question 0.6. Let Alice send Bob a message using a linear code V, and suppose e of the bits are garbled. Show that, if e <d, then Bob will be able to detect that an error has occurred and, if e <d/2, then Bob will be able to determine Alice's intended message.
Transcribed Image Text:Question 0.6. Let Alice send Bob a message using a linear code V, and suppose e of the bits are garbled. Show that, if e <d, then Bob will be able to detect that an error has occurred and, if e <d/2, then Bob will be able to determine Alice's intended message.
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