Complete Weight Enumerator of Linear Codes

[Sihuang Hu]

Hi,

I found that Sage is not able to compute the Complete Weight Enumerator of Linear Codes.
So I load magma to compute it:

sage: k.<a> = GF(2**2)
sage: MS = MatrixSpace(k,4,7)
sage: G  = MS([[1,1,1,0,0,0,0], [1,0,0,1,1,0,0], [0,1,0,1,0,1,0], [1,1,0,1,0,0,1]])
sage: C = LinearCode(G)
sage: magma.CompleteWeightEnumerator(C)
$.1^7 + 7*$.1^4*$.2^3 + 7*$.1^4*$.3^3 + 7*$.1^4*$.4^3 + 7*$.1^3*$.2^4 + 7*$.1^3*$.3^4 + 7*$.1^3*$.4^4 + 42*$.1^2*$.2^2*$.3^2*$.4 + 42*$.1^2*$.2^2*$.3*$.4^2 + 42*$.1^2*$.2*$.3^2*$.4^2 + 42*$.1*$.2^2*$.3^2*$.4^2 + $.2^7 + 7*$.2^4*$.3^3 + 7*$.2^4*$.4^3 + 7*$.2^3*$.3^4 + 7*$.2^3*$.4^4 + $.3^7 + 7*$.3^4*$.4^3 + 7*$.3^3*$.4^4 + $.4^7

Do anyone know how I can get the output of 'magma.CompleteWeightEnumerator(C)'
as the following form
e^7 + 7*e^4*x^3 + 7*e^4*y^3 + 7*e^4*z^3 + ...
In other words, display $.1 -> e, $.2 -> x, $.3 -> y, $.4 -> z.

Thanks,
Sihuang

[Vincent Delecroix]

Hello,

If it is just a matter of display you can use the method .replace() of strings

sage: sage: initial_string = "$.1 + 3 $.2"
sage: sage: initial_string.replace("$.1", "e").replace("$.2", "f")
'e + 3 f'

You can also have a look at
http://stackoverflow.com/questions/6116978/python-replace-multiple-strings
for multiple replacement.

To convert your magma polynomial p into a string just do str(p).

Vincent

2015-01-03 15:40 UTC+01:00, Sihuang Hu <husi...@gmail.com>:

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[Sihuang Hu]

Hi, Vincent.

What I want to do is to get a polynomial which is in the polynomial ring R.<e,x,y,z> = PolynomialRing(ZZ, 4).

Do you know how to do this?

Thanks,
Sihuang

在 2015年1月3日星期六UTC+1下午4时05分08秒，vdelecroix写道：

[Vincent Delecroix]

Hi Sihuang,

I see. I do not have magma, so my solution is certainly not optimal
but you can do a three steps conversion

magma polynomial ->
string in $.1, $.2, $.3 and $.4 ->
string in e, f, g, h ->
polynomial

To create the polynomial from a string it works out of the box

sage: R.<e,x,y,z> = PolynomialRing(ZZ, 4)
sage: string = '3 * e^2 + 2 * x * y + 13 * x'
sage: R(string)
3*e^2 + 2*x*y + 13*x

I hope that somebody with magma on his/her computer will come with a
better solution.

Vincent

2015-01-03 16:17 UTC+01:00, Sihuang Hu <husi...@gmail.com>:

> Hi, Vincent.
>
> What I want to do is to get a polynomial which is in the polynomial ring
> R.<e,x,y,z> = PolynomialRing(ZZ, 4).
>
> Do you know how to do this?
>
> Thanks,
> Sihuang
>
> 在 2015年1月3日星期六UTC+1下午4时05分08秒，vdelecroix写道：
>>
>> Hello,
>>
>> If it is just a matter of display you can use the method .replace() of
>> strings
>>
>> sage: sage: initial_string = "$.1 + 3 $.2"
>> sage: sage: initial_string.replace("$.1", "e").replace("$.2", "f")
>> 'e + 3 f'
>>
>> You can also have a look at
>> http://stackoverflow.com/questions/6116978/python-replace-multiple-strings
>>
>> for multiple replacement.
>>
>> To convert your magma polynomial p into a string just do str(p).
>>
>> Vincent
>>

>> 2015-01-03 15:40 UTC+01:00, Sihuang Hu <husi...@gmail.com <javascript:>>:

>> > email to sage-support...@googlegroups.com <javascript:>.

>> > To post to this group, send email to sage-s...@googlegroups.com

>> <javascript:>.

[Sihuang Hu]

It works. Thanks a lot.

Sihuang

在 2015年1月3日星期六UTC+1下午7时55分52秒，vdelecroix写道：