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Applied Algebra: Codes, Ciphers and Discrete Algorithms

Darel W. Hardy, Fred Richman, Carol L. Walker

Chapter 5

Error-Control Codes - all with Video Answers

Educators


Section 1

Weights and Hamming Distance

00:37

Problem 1

If you use pure guessing on a 10 -question true/false exam, what is the probability that you get them all right?

James Macpherson
James Macpherson
Numerade Educator
00:37

Problem 2

If you use pure guessing on a 10 -question true/false exam, what is the probability that you get at least 7 out of 10 ?

James Macpherson
James Macpherson
Numerade Educator

Problem 3

What is the minimum distance between codewords for the triple repetition code?

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10:39

Problem 4

What is the probability of no errors if 3 bits are transmitted through a binary symmetric channel with $p=0.05$ ?

Chris Trentman
Chris Trentman
Numerade Educator
10:39

Problem 5

What is the probability of exactly one error if 200 bits are transmitted through a binary symmetric channel with $p=0.0001$ ?

Chris Trentman
Chris Trentman
Numerade Educator

Problem 6

What is the probability of at least two errors if 1000 bits are transmitted through a binary symmetric channel with $p=0.001$ ?

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Problem 7

What is the expected number of errors if 1000 bits are transmitted through a binary symmetric channel with $p=0.001$ ?

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Problem 8

What is the minimum distance between the following collection of garbled sentences?
```
When trcnsmitthngddata, thery is always
tte pfssibhlity of error.
When transmittxng datae therj is zlwaps
the possibulity of xrror.
When trznspitting data, there is always
the possibility oe evyorg
Whfn tranymyttgnc data, nheri is always
the hossibility of error.
When transmitting data, dherexis alwahs
the jossicility of error.
```

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Problem 9

The garbled sentences in problem 8 were generated by assuming that the error rate was $1 / 10$. Explain why a minimum distance of 11 is reasonable.

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