Affirmation in Ternary Golay Codes theory
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There is an affirmation in Ternay Golay Codes Theory i don't get:
Let's supose we have $uin G_{12}$. Then, as far as we know $G_{12}$ is a self-dual code, so his generator matrix and his parity-check matrix are generator matrices of
$G_{12}$. Thus, if we write $u=(u_L,u_R)$ with $u_L,u_Rin V(6,3)$ we have that $w(u)=w(u_L)+w(u_R)$ and u is the sum of $w(u_L)$ rows of the generator matrix and $w(u_R)$ rows of the parity-check matrix.
I don't understand why is true the black sentence.
PD: We are supposing that $G=[I|B]$ and $H=[2B|I]$.
coding-theory
asked Nov 20 at 19:24
Lecter
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There is an affirmation in Ternay Golay Codes Theory i don't get:
Let's supose we have $uin G_{12}$. Then, as far as we know $G_{12}$ is a self-dual code, so his generator matrix and his parity-check matrix are generator matrices of
$G_{12}$. Thus, if we write $u=(u_L,u_R)$ with $u_L,u_Rin V(6,3)$ we have that $w(u)=w(u_L)+w(u_R)$ and u is the sum of $w(u_L)$ rows of the generator matrix and $w(u_R)$ rows of the parity-check matrix.
I don't understand why is true the black sentence.
PD: We are supposing that $G=[I|B]$ and $H=[2B|I]$.
coding-theory
asked Nov 20 at 19:24
Lecter
628
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
There is an affirmation in Ternay Golay Codes Theory i don't get:
Let's supose we have $uin G_{12}$. Then, as far as we know $G_{12}$ is a self-dual code, so his generator matrix and his parity-check matrix are generator matrices of
$G_{12}$. Thus, if we write $u=(u_L,u_R)$ with $u_L,u_Rin V(6,3)$ we have that $w(u)=w(u_L)+w(u_R)$ and u is the sum of $w(u_L)$ rows of the generator matrix and $w(u_R)$ rows of the parity-check matrix.
I don't understand why is true the black sentence.
PD: We are supposing that $G=[I|B]$ and $H=[2B|I]$.
coding-theory
asked Nov 20 at 19:24
Lecter
628
There is an affirmation in Ternay Golay Codes Theory i don't get:
Let's supose we have $uin G_{12}$. Then, as far as we know $G_{12}$ is a self-dual code, so his generator matrix and his parity-check matrix are generator matrices of
$G_{12}$. Thus, if we write $u=(u_L,u_R)$ with $u_L,u_Rin V(6,3)$ we have that $w(u)=w(u_L)+w(u_R)$ and u is the sum of $w(u_L)$ rows of the generator matrix and $w(u_R)$ rows of the parity-check matrix.
I don't understand why is true the black sentence.
PD: We are supposing that $G=[I|B]$ and $H=[2B|I]$.
coding-theory
coding-theory
asked Nov 20 at 19:24
Lecter
628
asked Nov 20 at 19:24
Lecter
628
asked Nov 20 at 19:24
Lecter
628
asked Nov 20 at 19:24
Lecter
628
asked Nov 20 at 19:24
Lecter
628
628
add a comment |
add a comment |
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