TY - JOUR
T1 - Quasi -symmetric designs with good blocks and intersection number one
AU - Mavron, Vassili C.
AU - McDonough, Thomas
AU - Schrikhande, M. S.
N1 - Mavron, Vassili; McDonough, T.P.; Schrikhande, M.S., (2003) 'Quasi -symmetric designs with good blocks and intersection number one', Designs Codes and Cryptography 28(2) pp.147-162
RAE2008
PY - 2003/3
Y1 - 2003/3
N2 - We show that a quasi-symmetric design with intersection numbers 1 and y > 1 and a good block belongs to one of three types: (a) it has the same parameters as PG 2(4, q), the design of points and planes in projective 4-space; (b) it is the 2-(23, 7, 21) Witt design; (c) its parameters may be written v = 1 + (( – 1) + 1)(y – 1) and k = 1 + (y – 1), where is an integer and > y 5, and the design induced on a good block is a 2-(k, y, 1) design. No design of type (c) is known; moreover, for large ranges of the parameters, it cannot exist for arithmetic reasons concerning the parameters. We show also that PG 2(4, q) is the only design of type (a) in which all blocks are good.
AB - We show that a quasi-symmetric design with intersection numbers 1 and y > 1 and a good block belongs to one of three types: (a) it has the same parameters as PG 2(4, q), the design of points and planes in projective 4-space; (b) it is the 2-(23, 7, 21) Witt design; (c) its parameters may be written v = 1 + (( – 1) + 1)(y – 1) and k = 1 + (y – 1), where is an integer and > y 5, and the design induced on a good block is a 2-(k, y, 1) design. No design of type (c) is known; moreover, for large ranges of the parameters, it cannot exist for arithmetic reasons concerning the parameters. We show also that PG 2(4, q) is the only design of type (a) in which all blocks are good.
KW - quasi-symmetric designs
KW - good blocks
KW - intersection numbers
U2 - 10.1023/A:1022536423514
DO - 10.1023/A:1022536423514
M3 - Article
SN - 0925-1022
VL - 28
SP - 147
EP - 162
JO - Designs, Codes and Cryptography
JF - Designs, Codes and Cryptography
IS - 2
ER -