1. Projective Two-Weight Codes
A linear code is called projective
if any two
of its coordinates are linearly independent, or in other words, if the
distance of its dual code is at least three. A code is called the two-weight
code if any nonzero codeword has a weight w1 or w2.
the link to search the online
database of two-weight codes. You are welcome to send me your
constructions of two-weight codes ( eric.chen at hkr.se ).
A strongly regular graph
with parameters (N, K, λ, μ) is a finite simple graph
on N vertices, regular of
degree K, and such that any two distinct vertices have λ
common neighbours when
they are adjacent and μ common neighbours when
they are not adjacent.
A projective two-weight code specifies a strongly regular graph.
Strongly Regular Graphs
A q-ary projective two-weight code specifies a
strongly regular graph. Let w1
suppose w1 < w2) be two weights of a
projective q-ary two-weight
[n, k] code. A strongly regular graph can be constructed as follows. The vertices of the graph are identified by the
codewords, and two
vertices x and y are adjacent if and only d(x, y) = w1.
The resulting strongly regular graph has parameters (N, K,
λ, μ ) given by :
N = qk,
K = n (q-1)
λ = K2 + 3K –q(w1 +
w2) – Kq(w1 + w2)
+ q2 w1w2
μ = q2
qk = K2 + K –Kq(w1 +
w2) + q2
 R. CALDERBANK AND W. M. KANTOR, "THE GEOMETRY OF TWO-WEIGHT CODES",
Bull. London Math. Soc. 18 (1986) 97-122