please help with exercise 1.3 and explain step by step Exercise 1.2Construct the sets Cn and Coo for the ternary code C = {02, 12, 120, 20, 21}.Do the same for C = {02, 12, 120, 21}.Exercise 1.3=Determine whether or not the codes C = {02, 12, 120, 20, 21} and C{02, 12, 120, 21} considered in Exercise 1.2 are uniquely decodable. If C isnot uniquely decodable, find a code-sequence which can be decoded in atleast two ways.

Answered: Exercise 1.3 Determine whether or not…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.7: Introduction To Coding Theory (optional)

Problem 4E

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please help with exercise 1.3 and explain step by step

Exercise 1.2
Construct the sets Cn and Coo for the ternary code C = {02, 12, 120, 20, 21}.
Do the same for C = {02, 12, 120, 21}.
Exercise 1.3
=
Determine whether or not the codes C = {02, 12, 120, 20, 21} and C
{02, 12, 120, 21} considered in Exercise 1.2 are uniquely decodable. If C is
not uniquely decodable, find a code-sequence which can be decoded in at
least two ways.

Expert Solution

Step 1

Exercise 1.3 asks us to determine whether the codes C = {02, 12, 120, 20, 21} and C = {02, 12, 120, 21} considered in Exercise 1.2 are uniquely decodable. If they are not uniquely decodable, we need to find a code-sequence which can be decoded in at least two ways.

To determine whether a code is uniquely decodable, we need to check if there is any code-sequence that can be decoded in two different ways. In other words, if we have a sequence of encoded symbols, we need to see if there is more than one way to decode that sequence into the original message.