Equivalent codes

Error

There was an error loading the page.

Contributors

Feedback

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

Christian Lawson-Perfect	said	Has some problems	2 years ago
Newcastle University Mathematics and Statistics	said	Ready to use	6 years, 7 months ago

History

○

Christian Lawson-Perfect commented 2 years ago

The variable testing condition is never satisfied, so something has changed.

○

Christian Lawson-Perfect 2 years ago

Gave some feedback: Has some problems

○

Christian Lawson-Perfect 6 years, 7 months ago

Published this.

○

Newcastle University Mathematics and Statistics 6 years, 7 months ago

Gave some feedback: Ready to use

○

Christian Lawson-Perfect 6 years, 7 months ago

Created this.

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

Question statement

Determine which of the following codes in $\mathbb{Z}_{\var{field_size}}^{\var{word_length}}$ are equivalent.

$\begin{align} C_1 &= \var{codes[code_order[0]]} & C_2 &= \var{codes[code_order[1]]} \\ C_3 &= \var{codes[code_order[2]]} & C_4 &= \var{codes[code_order[3]]} \\ C_5 &= \var{codes[code_order[4]]} & C_6 &= \var{codes[code_order[5]]} \\ C_7 &= \var{codes[code_order[6]]} & C_8 &= \var{codes[code_order[7]]} \\ \end{align}$

First, compute tables of Hamming distances for each of the codes, and then indicate which pairs of codes are equivalent in the grid at the bottom.

Give any introductory information the student needs.

			Name	Type	Generated Value

			word_length		Testing condition not satisfied
			field_size		Testing condition not satisfied
			num_words		Testing condition not satisfied
			base_codes		Testing condition not satisfied
			positional_permutations		Testing condition not satisfied
			symbolic_permutations		Testing condition not satisfied
			composed_permutations		Testing condition not satisfied
			equivalent_codes		Testing condition not satisfied
			codes		Testing condition not satisfied
			code_order		Testing condition not satisfied
			unshuffled_equivalence_matrix		Testing condition not satisfied
			equivalence_matrix		Testing condition not satisfied
			inverse_code_order		Testing condition not satisfied
			equivalence_indices		Testing condition not satisfied
			word_distances		Testing condition not satisfied
			equivalents_marking_matrix		Testing condition not satisfied

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
4

JME function reference

Description

Length of words in each code

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

Can an exam override the value of this variable?

→ Used by:

base_codes
positional_permutations
symbolic_permutations

Statement

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add
7. Gap Gap 6. Number entry
  Add
8. Gap Gap 7. Number entry
  Add
9. Gap Gap 8. Number entry
  Add
10. Gap Gap 9. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add
7. Gap Gap 6. Number entry
  Add
8. Gap Gap 7. Number entry
  Add
9. Gap Gap 8. Number entry
  Add
10. Gap Gap 9. Number entry
  Add
Part c) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add
7. Gap Gap 6. Number entry
  Add
8. Gap Gap 7. Number entry
  Add
9. Gap Gap 8. Number entry
  Add
10. Gap Gap 9. Number entry
  Add
Part d) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add
7. Gap Gap 6. Number entry
  Add
8. Gap Gap 7. Number entry
  Add
9. Gap Gap 8. Number entry
  Add
10. Gap Gap 9. Number entry
  Add
Part e) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add
7. Gap Gap 6. Number entry
  Add
8. Gap Gap 7. Number entry
  Add
9. Gap Gap 8. Number entry
  Add
10. Gap Gap 9. Number entry
  Add
Part f) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add
7. Gap Gap 6. Number entry
  Add
8. Gap Gap 7. Number entry
  Add
9. Gap Gap 8. Number entry
  Add
10. Gap Gap 9. Number entry
  Add
Part g) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add
7. Gap Gap 6. Number entry
  Add
8. Gap Gap 7. Number entry
  Add
9. Gap Gap 8. Number entry
  Add
10. Gap Gap 9. Number entry
  Add
Part h) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add
7. Gap Gap 6. Number entry
  Add
8. Gap Gap 7. Number entry
  Add
9. Gap Gap 8. Number entry
  Add
10. Gap Gap 9. Number entry
  Add
Part i) Match choices with answers

Gap-fill

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

$C_1$

	$\var{codes[code_order[0]][0]}$	$\var{codes[code_order[0]][1]}$	$\var{codes[code_order[0]][2]}$	$\var{codes[code_order[0]][3]}$
$\var{codes[code_order[0]][0]}$	Gap 0.
$\var{codes[code_order[0]][1]}$	Gap 1.	Gap 2.
$\var{codes[code_order[0]][2]}$	Gap 3.	Gap 4.	Gap 5.
$\var{codes[code_order[0]][3]}$	Gap 6.	Gap 7.	Gap 8.	Gap 9.

Advice

Begin by computing a table of Hamming distances for each code.

\[ C_1 \]

{distance_table(codes[code_order[0]])}

\[ C_2 \]

{distance_table(codes[code_order[1]])}

\[ C_3 \]

{distance_table(codes[code_order[2]])}

\[ C_4 \]

{distance_table(codes[code_order[3]])}

\[ C_5 \]

{distance_table(codes[code_order[4]])}

\[ C_6 \]

{distance_table(codes[code_order[5]])}

\[ C_7 \]

{distance_table(codes[code_order[6]])}

\[ C_8 \]

{distance_table(codes[code_order[7]])}

First, note that every code is equivalent to itself.

Two codes whose tables contain different numbers cannot be equivalent. Two codes whose tables contain the same numbers might be equivalent, but to prove equivalence you must find a composition of symbolic and positional permutations which map one code to the other.

$C_{\var{equivalence_indices[0][0]}}$ and $C_{\var{equivalence_indices[0][1]}}$ are equivalent: to obtain $C_{\var{inverse_code_order[5]+1}}$ from $C_{\var{inverse_code_order[0]+1}}$, {explain_permutation(composed_permutations[0])}

$C_{\var{equivalence_indices[1][0]}}$ and $C_{\var{equivalence_indices[1][1]}}$ are equivalent: to obtain $C_{\var{inverse_code_order[6]+1}}$ from $C_{\var{inverse_code_order[1]+1}}$, {explain_permutation(composed_permutations[1])}

$C_{\var{equivalence_indices[2][0]}}$ and $C_{\var{equivalence_indices[2][1]}}$ are equivalent: to obtain $C_{\var{inverse_code_order[7]+1}}$ from $C_{\var{inverse_code_order[2]+1}}$, {explain_permutation(composed_permutations[2])}

$C_{\var{inverse_code_order[3]+1}}$ and $C_{\var{inverse_code_order[4]+1}}$ are not equivalent to each other, or any of the other codes.

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?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Match choices with answers
Match choices with answers		Hasn't run yet

This question is used in the following exams:

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect commented 2 years ago

Christian Lawson-Perfect 2 years ago

Christian Lawson-Perfect 6 years, 7 months ago

Newcastle University Mathematics and Statistics 6 years, 7 months ago

Christian Lawson-Perfect 6 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value:

Parts

Gap-fill