Article
Group divisible designs, GBRDSDS and generalized weighing matrices
Faculty of Informatics - Papers (Archive)
Publication Date
1-1-1998
Abstract
We give new constructions for regular group divisible designs, pairwise balanced designs, generalized Bhaskar Rao supplementary difference sets and generalized weighing matrices. In particular if p is a prime power and q divides p - 1 we show the following exist;
(i) GDD (2(p2+p+1), 2(p2+p+1), rp2,2p2, λ1 = p2λ, λ2 = (p2-p)r, m=p2+p+1,n=2), r_+1,2;
(ii) GDD(q(p+1), q(p+1), p(q-1), p(q-1),λ1=(q-1)(q-2), λ2=(p-1)(q-1)2/q,m=q,n=p+1);
(iii) PBD(21,10;K),K={3,6,7} and PDB(78,38;K), K={6,9,45};
(iv) GW(vk,k2;EA(k)) whenever a (v,k,λ)-difference set exists and k is a prime power;
(v) PBIBD(vk2,vk2,k2,k2;λ1=0,λ2=λ,λ3=k) whenever a (v,k,λ)-difference set exists and k is a prime power;
(vi) we give a GW(21;9;Z3).
Disciplines
Citation Information
Dinesh G. Sarvate and Jennifer Seberry. "Group divisible designs, GBRDSDS and generalized weighing matrices" (1998) Available at: http://works.bepress.com/jseberry/360/
Dinesh Sarvate and Jennifer Seberry, Group divisible designs, GBRDSDS and generalized weighing matrices, Utilitas Mathematica, 54, (1998), 157-174.