#18960: Strongly Regular Graphs from two-weight codes
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Reporter: | Owner:
ncohen | Status: needs_review
Type: | Milestone: sage-6.9
enhancement | Resolution:
Priority: major | Merged in:
Component: graph | Reviewers:
theory | Work issues:
Keywords: | Commit:
Authors: | 606d15fbf46b427ed47a92e7250d75f4711cdd78
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/18960 |
Dependencies: |
#18948 |
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Comment (by dimpase):
Replying to [comment:12 ncohen]:
> Are you okay with the current state? I do not think that much confusion
can happen anymore, in its current form.
No, check the definition! It is about linear independence of
**coordinates**, not codewords. The definition, with details, is actually
from Delsarte's [4], where you see what coordinates are; [4] is a free
[http://www.sciencedirect.com/science/article/pii/0012365X72900246
download].
In a nutshell, take the matrix M with the **rows** consisting of the
codewords of C (it suffices to take any generating subset set of
codewords, if we talk about linear codes). Then the definition says that
every two **columns** of M are linearly independent.
Equivalently, they add, the dual code C* of C has minimal distance 3:
indeed, a linear dependence between two columns of M gives rise to a
weight 2 word w in C*, and thus the minimal distance at most 2 (take the
distance between all-0 word in C* and w).
Sorry for the confusion; this is indeed about a set of points in a
projective space, the space of columns of M---but not the set of codewords
of C...
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Ticket URL: <http://trac.sagemath.org/ticket/18960#comment:13>
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