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 -