Code Weight Theorem [on hold]

-1

So, I'm trying to proof a theorem that says:

Let $H$ be a parity-check matrix of a linear $C$ code.

Then $w(C) = d, d in mathbb{Z}$ if and only if any set of $d-1$ lines of H is linearly independent and there exists $d$ lines of $H$ that are linearly dependents.

Any leads?

edited 2 days ago

asked 2 days ago

Rodrigo Geaquinto Gonçalves

put on hold as off-topic by Morgan Rodgers, Paul Frost, Davide Giraudo, Shailesh, KReiser 2 days ago

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Morgan Rodgers, Paul Frost, Davide Giraudo, Shailesh, KReiser

If this question can be reworded to fit the rules in the help center, please edit the question.

1

Have you thought about it? Have you tried out a single example, to check (if) it's true, and to get a sense why?
– leonbloy
2 days ago

ALso, what is your definition of $w(C)$ ?
– leonbloy
2 days ago

w(C) is the minimum weight of a code. Taking a word from C, the weight of that word is the number of coordenates that are different from 0.
– Rodrigo Geaquinto Gonçalves
2 days ago

add a comment |

-1

So, I'm trying to proof a theorem that says:

Let $H$ be a parity-check matrix of a linear $C$ code.

Then $w(C) = d, d in mathbb{Z}$ if and only if any set of $d-1$ lines of H is linearly independent and there exists $d$ lines of $H$ that are linearly dependents.

Any leads?

edited 2 days ago

asked 2 days ago

Rodrigo Geaquinto Gonçalves

put on hold as off-topic by Morgan Rodgers, Paul Frost, Davide Giraudo, Shailesh, KReiser 2 days ago

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Morgan Rodgers, Paul Frost, Davide Giraudo, Shailesh, KReiser

If this question can be reworded to fit the rules in the help center, please edit the question.

1

Have you thought about it? Have you tried out a single example, to check (if) it's true, and to get a sense why?
– leonbloy
2 days ago

ALso, what is your definition of $w(C)$ ?
– leonbloy
2 days ago

w(C) is the minimum weight of a code. Taking a word from C, the weight of that word is the number of coordenates that are different from 0.
– Rodrigo Geaquinto Gonçalves
2 days ago

add a comment |

-1

So, I'm trying to proof a theorem that says:

Let $H$ be a parity-check matrix of a linear $C$ code.

Then $w(C) = d, d in mathbb{Z}$ if and only if any set of $d-1$ lines of H is linearly independent and there exists $d$ lines of $H$ that are linearly dependents.

Any leads?

edited 2 days ago

asked 2 days ago

Rodrigo Geaquinto Gonçalves

So, I'm trying to proof a theorem that says:

Let $H$ be a parity-check matrix of a linear $C$ code.

Then $w(C) = d, d in mathbb{Z}$ if and only if any set of $d-1$ lines of H is linearly independent and there exists $d$ lines of $H$ that are linearly dependents.

Any leads?

coding-theory

edited 2 days ago

asked 2 days ago

Rodrigo Geaquinto Gonçalves

edited 2 days ago

asked 2 days ago

Rodrigo Geaquinto Gonçalves

edited 2 days ago

asked 2 days ago

Rodrigo Geaquinto Gonçalves

asked 2 days ago

Rodrigo Geaquinto Gonçalves

asked 2 days ago

Rodrigo Geaquinto Gonçalves

put on hold as off-topic by Morgan Rodgers, Paul Frost, Davide Giraudo, Shailesh, KReiser 2 days ago

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Morgan Rodgers, Paul Frost, Davide Giraudo, Shailesh, KReiser

If this question can be reworded to fit the rules in the help center, please edit the question.

put on hold as off-topic by Morgan Rodgers, Paul Frost, Davide Giraudo, Shailesh, KReiser 2 days ago

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Morgan Rodgers, Paul Frost, Davide Giraudo, Shailesh, KReiser

If this question can be reworded to fit the rules in the help center, please edit the question.

1

Have you thought about it? Have you tried out a single example, to check (if) it's true, and to get a sense why?
– leonbloy
2 days ago

ALso, what is your definition of $w(C)$ ?
– leonbloy
2 days ago

w(C) is the minimum weight of a code. Taking a word from C, the weight of that word is the number of coordenates that are different from 0.
– Rodrigo Geaquinto Gonçalves
2 days ago

add a comment |

1

Have you thought about it? Have you tried out a single example, to check (if) it's true, and to get a sense why?
– leonbloy
2 days ago

ALso, what is your definition of $w(C)$ ?
– leonbloy
2 days ago

w(C) is the minimum weight of a code. Taking a word from C, the weight of that word is the number of coordenates that are different from 0.
– Rodrigo Geaquinto Gonçalves
2 days ago

Have you thought about it? Have you tried out a single example, to check (if) it's true, and to get a sense why?
– leonbloy
2 days ago

ALso, what is your definition of $w(C)$ ?
– leonbloy
2 days ago

w(C) is the minimum weight of a code. Taking a word from C, the weight of that word is the number of coordenates that are different from 0.
– Rodrigo Geaquinto Gonçalves
2 days ago

add a comment |

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