verifying G*(transpose(H)) = 0 for generator matrix G and parity check matrix H.
$begingroup$
I've got a non systematic generator matrix G given by,
G= [1 1 0 1 0 0 0;0 1 1 0 1 0 0;0 0 1 1 0 1 0;0 0 0 1 1 0 1]
I've converted this matrix by the following operations,
(1)exchanging C3 and C6
(2)exchanging C4 and C7
(3) adding R1+R2 and changing R1.
The obtained matrix is given by Gs=[1 0 0 0 1 1 1;0 1 0 0 1 1 0;0 0 1 0 0 1 1;0 0 0 1 1 0 1].The parity check matrix of Gs is Hs= [1 0 0 1 1 0 1;0 1 0 1 1 1 0;0 0 1 1 0 1 1].Now I'm not clear how to verify G*(transpose(H)) = 0. Should we undo the column operation in the H matrix? And the row spaces of which two matrices are orthogonal?It will be of great help if someone can help.Thanks.
coding-theory
asked Jan 6 at 9:59
math mathmath math
186
$endgroup$
add a comment |
$begingroup$
I've got a non systematic generator matrix G given by,
G= [1 1 0 1 0 0 0;0 1 1 0 1 0 0;0 0 1 1 0 1 0;0 0 0 1 1 0 1]
I've converted this matrix by the following operations,
(1)exchanging C3 and C6
(2)exchanging C4 and C7
(3) adding R1+R2 and changing R1.
The obtained matrix is given by Gs=[1 0 0 0 1 1 1;0 1 0 0 1 1 0;0 0 1 0 0 1 1;0 0 0 1 1 0 1].The parity check matrix of Gs is Hs= [1 0 0 1 1 0 1;0 1 0 1 1 1 0;0 0 1 1 0 1 1].Now I'm not clear how to verify G*(transpose(H)) = 0. Should we undo the column operation in the H matrix? And the row spaces of which two matrices are orthogonal?It will be of great help if someone can help.Thanks.
coding-theory
asked Jan 6 at 9:59
math mathmath math
186
$endgroup$
$begingroup$
Its really hard to read. Better have the matrix form.
$endgroup$
– Wuestenfux
Jan 6 at 14:59
add a comment |
$begingroup$
I've got a non systematic generator matrix G given by,
G= [1 1 0 1 0 0 0;0 1 1 0 1 0 0;0 0 1 1 0 1 0;0 0 0 1 1 0 1]
I've converted this matrix by the following operations,
(1)exchanging C3 and C6
(2)exchanging C4 and C7
(3) adding R1+R2 and changing R1.
The obtained matrix is given by Gs=[1 0 0 0 1 1 1;0 1 0 0 1 1 0;0 0 1 0 0 1 1;0 0 0 1 1 0 1].The parity check matrix of Gs is Hs= [1 0 0 1 1 0 1;0 1 0 1 1 1 0;0 0 1 1 0 1 1].Now I'm not clear how to verify G*(transpose(H)) = 0. Should we undo the column operation in the H matrix? And the row spaces of which two matrices are orthogonal?It will be of great help if someone can help.Thanks.
coding-theory
asked Jan 6 at 9:59
math mathmath math
186
$endgroup$
I've got a non systematic generator matrix G given by,
G= [1 1 0 1 0 0 0;0 1 1 0 1 0 0;0 0 1 1 0 1 0;0 0 0 1 1 0 1]
I've converted this matrix by the following operations,
(1)exchanging C3 and C6
(2)exchanging C4 and C7
(3) adding R1+R2 and changing R1.
The obtained matrix is given by Gs=[1 0 0 0 1 1 1;0 1 0 0 1 1 0;0 0 1 0 0 1 1;0 0 0 1 1 0 1].The parity check matrix of Gs is Hs= [1 0 0 1 1 0 1;0 1 0 1 1 1 0;0 0 1 1 0 1 1].Now I'm not clear how to verify G*(transpose(H)) = 0. Should we undo the column operation in the H matrix? And the row spaces of which two matrices are orthogonal?It will be of great help if someone can help.Thanks.
coding-theory
coding-theory
asked Jan 6 at 9:59
math mathmath math
186
asked Jan 6 at 9:59
math mathmath math
186
asked Jan 6 at 9:59
math mathmath math
186
asked Jan 6 at 9:59
math mathmath math
186
asked Jan 6 at 9:59
math mathmath math
186
186
$begingroup$
Its really hard to read. Better have the matrix form.
$endgroup$
– Wuestenfux
Jan 6 at 14:59
add a comment |
$begingroup$
Its really hard to read. Better have the matrix form.
$endgroup$
– Wuestenfux
Jan 6 at 14:59
$begingroup$
Its really hard to read. Better have the matrix form.
$endgroup$
– Wuestenfux
Jan 6 at 14:59
$begingroup$
Its really hard to read. Better have the matrix form.
$endgroup$
– Wuestenfux
Jan 6 at 14:59
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3063668%2fverifying-gtransposeh-0-for-generator-matrix-g-and-parity-check-matrix-h%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3063668%2fverifying-gtransposeh-0-for-generator-matrix-g-and-parity-check-matrix-h%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Its really hard to read. Better have the matrix form.
$endgroup$
– Wuestenfux
Jan 6 at 14:59