Find a parity check matrix for a linear code

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Christian Lawson-Perfect	said	Should not be used	1 year, 11 months ago
Newcastle University Mathematics and Statistics	said	Ready to use	6 years, 7 months ago

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Christian Lawson-Perfect commented 1 year, 11 months ago

There's a custom JS marking script which doesn't work. It should be replaced with a JME marking algorithm.

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Christian Lawson-Perfect 1 year, 11 months ago

Gave some feedback: Should not be used

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Christian Lawson-Perfect 6 years, 7 months ago

Published this.

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Newcastle University Mathematics and Statistics 6 years, 7 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 6 years, 7 months ago

Created this.

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Question statement

Find a parity check matrix $\mathrm{H}$ for the {nary} code $C$ with generator matrix

$\mathrm{G} =\var{G}$

Give any introductory information the student needs.

			Name	Type	Generated Value

field_size	integer	5
nary	string	$5$-ary
dimension	integer	3
word_length	integer	6
dual_dimension	integer	3
A	list	List of 3 items
M	list	List of 3 items
g_words	list	List of 3 items
g	matrix	Matrix of size 3×6
G_dual	matrix	Matrix of size 3×6

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Generated value: `integer`

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$\mathrm{H} = $ Unnamed gap

Advice

First, row-reduce $\mathrm{G}$ to obtain a standard generator matrix $\mathrm{M}$ for the code

\[ \mathrm{G}' = \var{codeword_matrix(M)} \]

This is in the form $(\mathrm{I}_{\var{dimension}}|\mathrm{A})$. A parity check matrix is then $(-\mathrm{A^T}|\mathrm{I}_{\var{word_length}-\var{dimension}})$, i.e.

\[ \mathrm{H} = \var{G_dual} \]

Note that this is just one possible parity-check matrix. In general any basis for the dual code $C^{\bot}$ would do for the rows of the parity-check matrix.

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Find a parity check matrix for a linear code

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Christian Lawson-Perfect commented 1 year, 11 months ago

Christian Lawson-Perfect 1 year, 11 months 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

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Generated value: `integer`

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Find a parity check matrix for a linear code

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect commented 1 year, 11 months ago

Christian Lawson-Perfect 1 year, 11 months 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: integer

Parts

Gap-fill

Generated value: `integer`