NEW INFINITE FAMILIES OF 3-DESIGNS FROM PREPARATA CODES OVER Z(4)(1)

Abstract

We consider t-designs constructed from codewords in the Preparata code P-m over Z(4). A new approach is given to prove that the support (size 5) of minimum Lee weight codewords form a simple 3-design for any odd integer m greater than or equal to 3. We also show that the support of codewords with support size 6 form four new families of simple 3-designs, with parameters (2(m),6,2(m) - 8), (2(m), 6, 5 . (2(m-1) - 4)), (2(m), 6, 20 . (2(m-1) - 4)/3) and (2(m), 6, 18 . (2(m-1) - 4)), for any odd integer m greater than or equal to 5. Codewords with support size 7 are also investigated by computer search. (C) 1999 Elsevier Science B.V. All rights reserved.