TY - JOUR

T1 - On affine designs and Hadamard designs with line spreads

AU - McDonough, Thomas

AU - Mavron, V. C.

AU - Tonchev, V. D.

N1 - V.C.Mavron, T.P. McDonough and V.D. Tonchev, On affine designs and Hadamard designs with line spreads. Discrete Mathematics
Volume 308, Issue 13, 6 July 2008, Pages 2742-2750.

PY - 2008/7/6

Y1 - 2008/7/6

N2 - Rahilly [On the line structure of designs, Discrete Math. 92 (1991) 291–303] described a construction that relates any Hadamard design H on 4^m-1 points with a line spread to an affine design having the same parameters as the classical design of points and hyperplanes in AG(m,4). Here it is proved that the affine design is the classical design of points and hyperplanes in AG(m,4) if, and only if, H is the classical design of points and hyperplanes in PG(2m-1,2) and the line spread is of a special type. Computational results about line spreads in PG(5,2) are given. One of the affine designs obtained has the same 2-rank as the design of points and planes in AG(3,4), and provides a counter-example to a conjecture of Hamada [On the p-rank of the incidence matrix of a balanced or partially balanced incomplete block design and its applications to error-correcting codes, Hiroshima Math. J. 3 (1973) 153–226].

AB - Rahilly [On the line structure of designs, Discrete Math. 92 (1991) 291–303] described a construction that relates any Hadamard design H on 4^m-1 points with a line spread to an affine design having the same parameters as the classical design of points and hyperplanes in AG(m,4). Here it is proved that the affine design is the classical design of points and hyperplanes in AG(m,4) if, and only if, H is the classical design of points and hyperplanes in PG(2m-1,2) and the line spread is of a special type. Computational results about line spreads in PG(5,2) are given. One of the affine designs obtained has the same 2-rank as the design of points and planes in AG(3,4), and provides a counter-example to a conjecture of Hamada [On the p-rank of the incidence matrix of a balanced or partially balanced incomplete block design and its applications to error-correcting codes, Hiroshima Math. J. 3 (1973) 153–226].

U2 - 10.1016/j.disc.2006.06.039

DO - 10.1016/j.disc.2006.06.039

M3 - Article

SN - 0012-365X

VL - 308

SP - 2742

EP - 2750

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 13

ER -