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
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