|
Search: id:A000952
|
|
|
| A000952 |
|
Orders n == 2 (mod 4) of conference matrices. (Formerly M1574 N0615)
|
|
+0 5
|
|
| 2, 6, 10, 14, 18, 26, 30, 38, 42, 46, 50, 54, 62
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
A conference matrix of order n is an n X n {-1,0,+1} matrix A such that A A' = (n-1)I.
If n == 2 (mod 4) then a necessary condition is that n-1 is a sum of 2 squares. It is conjectured that this condition is also sufficient. If n == 2 mod 4 and n-1 is a prime or prime power the condition is automatically satisfied.
|
|
REFERENCES
|
V. Belevitch, Conference matrices and Hadamard matrices, Ann. Soc. Scientifique Bruxelles, 82 (I) (1968), 13-32.
CRC Handbook of Combinatorial Designs, 1996, Chapter 52.
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 56.
|
|
LINKS
|
Joerg Arndt, Some relevant gp programs
|
|
EXAMPLE
|
The essentially unique conference matrix of order 6:
0 +1 +1 +1 +1 +1
+1 0 +1 -1 -1 +1
+1 +1 0 +1 -1 -1
+1 -1 +1 0 +1 -1
+1 -1 -1 +1 0 +1
+1 +1 -1 -1 +1 0
|
|
CROSSREFS
|
Sequence in context: A122905 A132417 A103747 this_sequence A039956 A118369 A082816
Adjacent sequences: A000949 A000950 A000951 this_sequence A000953 A000954 A000955
|
|
KEYWORD
|
nonn,hard,nice
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
66 seems to be the smallest order for which it is not known if a matrix exists.
Edited by njas, Mar 13 2008, Mar 16 2008
|
|
|
Search completed in 0.002 seconds
|