Understanding the weight enumerator of the Ternary Golay code.
$begingroup$
Im trying to calculate the weight enumerator of the ternay Golay Code $mathcal{G}_{11}$, using help from this paper.
I understand how we get $A_0$ and $A_5$, but not $A_6$.
In the proof of the second page, it says that $$2^4cdotbinom{11}{4}=A_6binom{6}{4}+A_5binom{5}{4}+132cdotbinom{5}{3}cdot 2$$
I understand why we have the first 2 terms of the sum , but I dont get the last one. I assume the 132 comes from the number of words of $A_5$, but what about the $binom{5}{3}cdot 2$?
Any help would be appreciated!
PD: I know $mathcal{G}_{11}$ is the punctured code of $mathcal{G}_{12}$, can we obtain $mathcal{G}_{11}$ using $mathcal{G}_{11}$?
abstract-algebra coding-theory combinatory-logic
asked Dec 7 '18 at 10:53
shurohigeshurohige
63
$endgroup$
add a comment |
$begingroup$
Im trying to calculate the weight enumerator of the ternay Golay Code $mathcal{G}_{11}$, using help from this paper.
I understand how we get $A_0$ and $A_5$, but not $A_6$.
In the proof of the second page, it says that $$2^4cdotbinom{11}{4}=A_6binom{6}{4}+A_5binom{5}{4}+132cdotbinom{5}{3}cdot 2$$
I understand why we have the first 2 terms of the sum , but I dont get the last one. I assume the 132 comes from the number of words of $A_5$, but what about the $binom{5}{3}cdot 2$?
Any help would be appreciated!
PD: I know $mathcal{G}_{11}$ is the punctured code of $mathcal{G}_{12}$, can we obtain $mathcal{G}_{11}$ using $mathcal{G}_{11}$?
abstract-algebra coding-theory combinatory-logic
asked Dec 7 '18 at 10:53
shurohigeshurohige
63
$endgroup$
add a comment |
$begingroup$
Im trying to calculate the weight enumerator of the ternay Golay Code $mathcal{G}_{11}$, using help from this paper.
I understand how we get $A_0$ and $A_5$, but not $A_6$.
In the proof of the second page, it says that $$2^4cdotbinom{11}{4}=A_6binom{6}{4}+A_5binom{5}{4}+132cdotbinom{5}{3}cdot 2$$
I understand why we have the first 2 terms of the sum , but I dont get the last one. I assume the 132 comes from the number of words of $A_5$, but what about the $binom{5}{3}cdot 2$?
Any help would be appreciated!
PD: I know $mathcal{G}_{11}$ is the punctured code of $mathcal{G}_{12}$, can we obtain $mathcal{G}_{11}$ using $mathcal{G}_{11}$?
abstract-algebra coding-theory combinatory-logic
asked Dec 7 '18 at 10:53
shurohigeshurohige
63
$endgroup$
Im trying to calculate the weight enumerator of the ternay Golay Code $mathcal{G}_{11}$, using help from this paper.
I understand how we get $A_0$ and $A_5$, but not $A_6$.
In the proof of the second page, it says that $$2^4cdotbinom{11}{4}=A_6binom{6}{4}+A_5binom{5}{4}+132cdotbinom{5}{3}cdot 2$$
I understand why we have the first 2 terms of the sum , but I dont get the last one. I assume the 132 comes from the number of words of $A_5$, but what about the $binom{5}{3}cdot 2$?
Any help would be appreciated!
PD: I know $mathcal{G}_{11}$ is the punctured code of $mathcal{G}_{12}$, can we obtain $mathcal{G}_{11}$ using $mathcal{G}_{11}$?
abstract-algebra coding-theory combinatory-logic
abstract-algebra coding-theory combinatory-logic
asked Dec 7 '18 at 10:53
shurohigeshurohige
63
asked Dec 7 '18 at 10:53
shurohigeshurohige
63
asked Dec 7 '18 at 10:53
shurohigeshurohige
63
asked Dec 7 '18 at 10:53
shurohigeshurohige
63
asked Dec 7 '18 at 10:53
shurohigeshurohige
63
63
add a comment |
add a comment |
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