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authorRelease Manager <release@sagemath.org>2015-08-05 12:52:26 +0200
committerVolker Braun <vbraun.name@gmail.com>2015-08-05 12:52:26 +0200
commitb435c030ebb82c1fc39963944867a5bb0bcaa08e (patch)
tree48e800a62f8f824a8d79707e8deb8a3080bda70b
parentTrac #18948: Strongly Regular Graphs database (diff)
parenttrac #18960: Merged with updated #18948 (diff)
Trac #18960: Strongly Regular Graphs from two-weight codes
This ticket adds several constructions of strongly regular graphs from two-weight codes. The data used here has been provided by Eric Chen, using information available on his database of two-weight codes: http://moodle.tec.hkr.se/~chen/research/2-weight-codes/search.php Nathann URL: http://trac.sagemath.org/18960 Reported by: ncohen Ticket author(s): Nathann Cohen Reviewer(s): Dima Pasechnik
-rw-r--r--src/sage/graphs/strongly_regular_db.pyx535
1 files changed, 534 insertions, 1 deletions
diff --git a/src/sage/graphs/strongly_regular_db.pyx b/src/sage/graphs/strongly_regular_db.pyx
index 9bd44a2a..19620b0 100644
--- a/src/sage/graphs/strongly_regular_db.pyx
+++ b/src/sage/graphs/strongly_regular_db.pyx
@@ -37,6 +37,9 @@ from sage.graphs.generators.smallgraphs import HigmanSimsGraph
from sage.graphs.generators.smallgraphs import LocalMcLaughlinGraph
from sage.graphs.graph import Graph
from libc.math cimport sqrt
+from sage.matrix.constructor import Matrix
+from sage.rings.finite_rings.constructor import FiniteField as GF
+from sage.coding.linear_code import LinearCode
cdef dict _brouwer_database = None
@@ -298,6 +301,521 @@ def SRG_280_135_70_60():
g.relabel()
return g
+def strongly_regular_from_two_weight_code(L):
+ r"""
+ Return a strongly regular graph from a two-weight code.
+
+ A code is said to be a *two-weight* code the weight of its nonzero codewords
+ (i.e. their number of nonzero coordinates) can only be one of two integer
+ values `w_1,w_2`. It is said to be *projective* if the minimum weight of the
+ dual code is `\geq 3`. A strongly regular graph