On Thursday, July 13, 2017 at 11:43:18 AM UTC+1, David Joyner wrote:
>
> On Thu, Jul 13, 2017 at 5:59 AM, 'B. L.' via sage-devel
> <sage-devel@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.
>
> 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...
>
> > 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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