Hamming's square code

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Newcastle University Mathematics and Statistics

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6 years, 8 months ago

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Christian Lawson-Perfect 6 years, 8 months ago

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Newcastle University Mathematics and Statistics 6 years, 8 months ago

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Christian Lawson-Perfect 6 years, 8 months ago

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Question statement

A binary string was encoded using Hamming's square code, and then transmitted.

The string $\var{received}$ was received.

Give any introductory information the student needs.

			Name	Type	Generated Value

num_codewords	integer	2
original_words	list	List of 2 items
encoded_original_words	list	List of 2 items
error_positions	list	[ 0, 6 ]
received_words	list	List of 2 items
original	codeword	codeword("10100010",2)
received	codeword	codeword("001101000000101001",2)

Automatically regenerate variables?

Name

Data type

Value

(a number)

Description

Number of words in the message

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Match text pattern
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Assuming that the received message contains at most one error per codeword, correct any errors, and then decode to find the original binary string.

Original message: Unnamed gap

Advice

Since we are using the Hamming square code, each encoded code word is of length $9$. We received $18$ digits, so we have $2$ words to check and decode, $\var{received_words[0]}$ and $\var{received_words[1]}$.

Checking the received word $\var{received_words[0]}$

Put this word into a square array.

{check_array(received_words[0])}

Since we know that at most one error has occurred we can decode as follows:

{error_description(received_words[0])}

Checking the received word $\var{received_words[1]}$

Put this word into a square array.

{check_array(received_words[1])}

Since we know that at most one error has occurred we can decode as follows:

{error_description(received_words[1])}

Putting these decoded messages together, we obtain $\var{original}$ as the answer.

Give a worked solution to the whole question.

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Match text pattern
Match text pattern		Hasn't run yet

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 6 years, 8 months ago

Newcastle University Mathematics and Statistics 6 years, 8 months ago

Christian Lawson-Perfect 6 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Hamming's square code

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 6 years, 8 months ago

Newcastle University Mathematics and Statistics 6 years, 8 months ago

Christian Lawson-Perfect 6 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`