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.
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.
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
Related questions
Question
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e663e5c-100c-4e3b-8b5b-7e174f02ab65%2Fcf827a39-c8e7-4803-82a6-ac2ea52836dc%2F9cdzrq_processed.png&w=3840&q=75)
Transcribed Image Text: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
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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.
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