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WorksheetsGEMATMW - Coding Theory
Total questions: 21
Worksheet time: 12mins
Which of the following is the field that is aimed at the construction of error-correcting codes?
Coding Theory
Cryptography
Computer Science
Digital Communications
What is the process of reducing the size of an electronic file for storage or transmission?
Decompression
Compression
Depression
Encoding
Decoding
Who is known for his significant contribution to information theory, part of which is coding theory, and is credited for the idea of using redundancy to add reliability to information?
Alan Turing
Claude Shannon
Richard Hamming
Whitfield Diffie
Mariah Carey
Which of the following are not the main goals of coding theory?
Error-detection
Error-correction
Transmission of Data
Confidentiality
Digital Signature
Which of the following are the main goals of coding theory?
Error Correction
Error Detection
Source Encoding
Source Decoding
Non-repudation
The following are even parity, except...
0000000
10101011
10101010
11111111
C = {01011010, 11000001, 01010101}. Up to how many errors can the code correct?
1
2
3
4
5
Up to how many errors can a code with a minimum distance of 20 correct?
Nine
Eighteen
Nineteen
Ten
Eleven
Suppose 11111 00111 11000 00001 is the message received (suppose a repetition code with every bit repeated 5 times is used). What do you think is the original codeword sent?
11111 11111 00000 00000
11111 0011111 11000 00001
11111 11111 11111 11111
11111 00000 00000 00000
00000 00000 00000 00000
After applying repetition code where every bit is repeated thrice, the received word is D(r) = 111 000 010 111 000 110 111 111. The corresponding original message sent is...
10010111
10110111
10010011
10110011
None of the Choices
A code can detect up to eight errors. What should be its smallest minimum distance?
Nine
Fourteen
Sixteen
Fifteen
Nineteen
A code can correct up to _____ errors and detect up to _____ errors if it has a minimum Hamming distance of twenty.
19; 9
9; 19
10; 19
19; 10
None of the Choices
The length of the binary word 01010101011 is...
Eleven
Seven
Eight
Five
Ten
The hamming distance, d(x,y), of any two binary strings x and y satisfy each of the following properties.
d(x,y) = d(y,x)
d(x,y) = 0 if and only if x = y
d(x,y) ≥ 0
d(x,y) ≥ d(x,z) + d(z,y)
Bananas
A codeword that is of odd parity is...
11111111
0000000
10101011
10101010
Which of the following received word is sure to contain at least one error (suppose an even parity code is used to send a message across a noisy channel)?
10101011
000000
111111
001111
Which of the following received word is free of any error (suppose a binary message word is to encoded using repetition code where every bit is to be repeated thrice)?
111 000 111 000
111 001 000 111
101 101 101 101
111 101 111 000
None of the Choices (except this, of course)
If a code can correct up to seven errors, what should be its smallest minimum distance?
Fifteen
Fourteen
Seven
Sixteen
Let C = {0000, 1100, 0011, 1111} be a code. Suppose Jose sends a message and Emilio received the binary word y = 1000. Which code word do you think did Jose send?
The error cannot be corrected
0011
0000
1111
1100
If a code can detect up to eight errors, what should be its smallest minimum distance?
Nine
Fourteen
Nineteen
Sixteen
The following are odd parity codes, except...
{000, 101, 011}
{001, 101, 011}
{001, 111, 100}
{000, 111, 101}
