Find all words within given Hamming distance

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Content created by Newcastle University :

Newcastle University Mathematics and Statistics

said

Ready to use

6 years, 8 months ago

History

○

Christian Lawson-Perfect 6 years, 8 months ago

Published this.

○

Newcastle University Mathematics and Statistics 6 years, 8 months ago

Gave some feedback: Ready to use

○

Christian Lawson-Perfect 6 years, 8 months ago

Created this.

There is only one version of this question that you have access to.

Question statement

Find all words $w \in \mathbb{Z}_{\var{field_size}}^{\var{word_length}}$ for which $d_\mathrm{H}(w,\var{base_word}) = \var{radius}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

word_length	integer	4
field_size	integer	2
base_word	codeword	codeword("1111",2)
radius	integer	1
sphere	list	List of 4 items
sphere_string	string	0111, 1011, 1101, 1110

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(3..6)

JME function reference

Description

Length of words

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

Match text pattern

Match text pattern

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

Enter your answer as a list of codewords, separated by commas. For example: 0000, 0001, 0002.

Marks

Match test

Answer pattern

Display answer

Show correct answer on reveal?

Show score feedback icon?

Advanced settings

Must the answer be in the correct case?

Advice

Each word $w$ must differ from the word $\var{base_word}$ in $\var{radius}$ {pluralise(radius,"place","places")}.

There are $\simplify{comb({word_length},{radius}) = {comb(word_length,radius)}}$ ways of choosing $\var{radius}$ {pluralise(radius,"digit","digits")} to change, and $\var{field_size}-1 = \var{field_size-1}$ {pluralise(field_size-1,"choice","choices")} for each changed digit.

That means that there are $\simplify[]{{comb(word_length,radius)}*{field_size-1}^{radius}} = \var{comb(word_length,radius)*(field_size-1)^radius}$ words $w$ with $d_\mathrm{H}(w,\var{base_word}) = \var{radius}$.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

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

This question is used in the following exams:

Loading...

Error

Find all words within given Hamming distance

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

Match text pattern

Advanced settings

Loading...

Error

Find all words within given Hamming distance

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

Match text pattern

Advanced settings

Generated value: `integer`