Two issues about the coding theory method "weight_enumerator"

[B. L.]

Dear Sage-Developers,

I'd like to report two issues that I came across when working with the coding theory classes of SAGE.

1. The Sage Reference Manual: Coding Theory, Release 7.6 [1] explains on p. 31:
   weight_enumerator [...] This is the bivariate, homogeneous polynomial in 𝑥 and 𝑦 whose coefficient to x^iy^{n-i} is the number of codewords of 𝑠𝑒𝑙𝑓 of Hamming weight 𝑖. Here, 𝑛 is the length of 𝑠𝑒𝑙𝑓.
   Actually, Sage returns another polynomial, namely the polynomial in 𝑥 and 𝑦 whose coefficient to x^{n-i}y^i is the number of codewords of 𝑠𝑒𝑙𝑓 of Hamming weight 𝑖. (So the roles of x and y are interchanged).
   This can be directly with C.weight_enumerator?? in the example below [2].
   
   I suggest to either change the description in the reference or to alter the code in Sage.
   
   
2. The function weight_enumerator(bivariate=False) returns the evaluation of the the above polynomial for y=1. Should't it be (in the current version) the evaluation with x=1? In other words: Wouldn't one expect a polynomial in x (or y) whose coefficient to x^i (or y^i) is the number of codewords of 𝑠𝑒𝑙𝑓 of Hamming weight 𝑖?
   The example below [2] illustrates my point: The code has four codewords, one of weight 0, two of weight 3, one of weiht 4. Sage gives x^5 + 2*x^2 + x as the univariate weight enumerator. I would have expected either 1 + 2*x^3 + x^4 or 1 + 2*y^3 + y^4.
   
   If you agree, I suggest to alter the code accordingly.
   

Kind regards
Barbara
PS: I tested the code with Sage version 7.6 on an iMac.


[1] http://doc.sagemath.org/pdf/en/reference/coding/coding.pdf

[2] Sage code for  the SageMathCell

C= LinearCode(Matrix(GF(2),2,5, [[1,1,0,1,0], [0,0,1,1,1]]))
print C.list()
print C.spectrum()
print C.weight_enumerator()
print C.weight_enumerator(bivariate=False)
C.weight_enumerator??

http://sagecell.sagemath.org/?z=eJxztlXwycxLTSxyzk9J1fBNLCnKrNBwd9Mw0tQx0jHVUYiONtQx1DEA4VggzwDMBMLYWE1NXq6Cosy8EgVnvZzM4hINJH5xQWpySVFpLrJYeWpmekZJfGpeaW5qUWJJfhF-yaTMssSizMSSVFu3xJziVKBaLKrs7QGIgD2K&lang=sage

[David Joyner]

On Thu, Jul 13, 2017 at 5:59 AM, 'B. L.' via sage-devel
<sage-...@googlegroups.com> wrote:
> Dear Sage-Developers,
>
> I'd like to report two issues that I came across when working with the
> coding theory classes of SAGE.
>
> The Sage Reference Manual: Coding Theory, Release 7.6 [1] explains on p. 31:
> weight_enumerator [...] This is the bivariate, homogeneous polynomial in 𝑥
> and 𝑦 whose coefficient to x^iy^{n-i} is the number of codewords of
> 𝑠𝑒𝑙𝑓 of Hamming weight 𝑖. Here, 𝑛 is the length of 𝑠𝑒𝑙𝑓.
> Actually, Sage returns another polynomial, namely the polynomial in 𝑥 and
> 𝑦 whose coefficient to x^{n-i}y^i is the number of codewords of 𝑠𝑒𝑙𝑓 of
> Hamming weight 𝑖. (So the roles of x and y are interchanged).
> This can be directly with C.weight_enumerator?? in the example below [2].
>
> I suggest to either change the description in the reference or to alter the
> code in Sage.
>

I'd propose just switching the x,y in the code:

(1) On line 3503 of linear_code.py, change "return
sum(spec[i]*x**(n-i)*y**i for i in range(n+1))" to "return
sum(spec[i]*x**(i)*y**(n-i) for i in range(n+1))"

(2) On line 3507, change "return sum(spec[i]*x**(n-i) for i in
range(n+1))" to "return sum(spec[i]*x**(i) for i in range(n+1))"

(3) Some of the examples may change accordingly.

This mistake could be my fault, since I wrote the original version
(long long ago). Unfortunately, I lack the git skills to submit a
patch.

> The function weight_enumerator(bivariate=False) returns the evaluation of
> the the above polynomial for y=1. Should't it be (in the current version)
> the evaluation with x=1? In other words: Wouldn't one expect a polynomial in
> x (or y) whose coefficient to x^i (or y^i) is the number of codewords of
> 𝑠𝑒𝑙𝑓 of Hamming weight 𝑖?
> The example below [2] illustrates my point: The code has four codewords, one
> of weight 0, two of weight 3, one of weiht 4. Sage gives x^5 + 2*x^2 + x as
> the univariate weight enumerator. I would have expected either 1 + 2*x^3 +
> x^4 or 1 + 2*y^3 + y^4.
>
> If you agree, I suggest to alter the code accordingly.
>
> Kind regards
> Barbara
> PS: I tested the code with Sage version 7.6 on an iMac.
>
>
> [1] http://doc.sagemath.org/pdf/en/reference/coding/coding.pdf
>
> [2] Sage code for the SageMathCell
>
> C= LinearCode(Matrix(GF(2),2,5, [[1,1,0,1,0], [0,0,1,1,1]]))
> print C.list()
> print C.spectrum()
> print C.weight_enumerator()
> print C.weight_enumerator(bivariate=False)
> C.weight_enumerator??
>
> http://sagecell.sagemath.org/?z=eJxztlXwycxLTSxyzk9J1fBNLCnKrNBwd9Mw0tQx0jHVUYiONtQx1DEA4VggzwDMBMLYWE1NXq6Cosy8EgVnvZzM4hINJH5xQWpySVFpLrJYeWpmekZJfGpeaW5qUWJJfhF-yaTMssSizMSSVFu3xJziVKBaLKrs7QGIgD2K&lang=sage
>

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[Dima Pasechnik]

A patch can be produced by

git diff > stuff.patch

It would be great if you opened a ticket and posted this diff as an attachment...

 

 

> email to sage-devel+unsubscribe@googlegroups.com.

[Johan S. H. Rosenkilde]

Thanks a lot for reporting! We *really* appreciate any feedback from
using Sage in classes: on bugs, designs and feature requests.

This bug is now #23433. I'll push a patch momentarily.

Best,
Johan Rosenkilde

>> > email to sage-devel+...@googlegroups.com.

[David Joyner]

On Fri, Jul 14, 2017 at 5:35 AM, Johan S. H. Rosenkilde
<mail...@atuin.dk> wrote:
> Thanks a lot for reporting! We *really* appreciate any feedback from
> using Sage in classes: on bugs, designs and feature requests.
>
> This bug is now #23433. I'll push a patch momentarily.
>

Thank you, Johan!

> Best,
> Johan Rosenkilde
>
>

...

>>>
>>> This mistake could be my fault, since I wrote the original version
>>> (long long ago). Unfortunately, I lack the git skills to submit a
>>> patch.
>>>

...

[B. L.]

Thank you for replying and submitting a ticket so promptly!
Barbara