Then {Ablb e GF(q)*} is an (h, q - 1, q)-DDS. Proof. Clearly, there are (q - 1) sets Ab, they are disjoint, and each contains q ele- ments: abi may be defined by ~abj ...
DISCRETE MATHEMATICS ELSEVIER
Discrete Mathematics 175 (1997) 69 77
Disjoint sets of distinct
sum
sets 1
W e n d e Chen a, Torleiv Klove b'* Institute of Systems Sciences, Academia Sinica, Beijing 100080, China t,Department of lnlormatics, UniversiO, of Bergen, Hogteknologisenteret, N-5020 Bergen, .'~?n'wav Received 19 October 1993; revised 21 March 1996
Abstract An (h, J)-distinct sum set is a set of J integers such that all sums of h elements (repetitions allowed) are distinct. An (h, I, J)-set of disjoint distinct sum sets is a set of I disjoint (h, J)distinct sum sets with positive elements. A number of constructions of such sets are given.
Kevwords." Distinct sum set; Intermodulation interference
1. Introduction Babcock [2] studied radio systems having frequencies w i t h o u t i n t e r m o d u l a t i o n interference. To avoid i n t e r m o d u l a t i o n interference of order 2h - 1 a n d less, his c o n s t r u c t i o n required sets such that all sums of h elements from the set are distinct. In our n o t a t i o n such a set of size J is called an (h, J)-DS or an (h, 1, J)-DDS. It is also k n o w n as a finite Bh-set. Such sets have been studied in a n u m b e r of contexts, a n d for h = 2 also u n d e r various other names, see e.g. [1, 3, 5, 14, 16, 19]. A generalization of the p r o b l e m was considered by C h e n [9]. He considered a mobile radio system for a collection of I areas, a n d w i t h o u t i n t e r m o d u l a t i o n interference of order up to 2h - 1 within each area. His c o n s t r u c t i o n requires a set of I disjoint (h, J)-distinct sum sets with positive elements (in our n o t a t i o n : an (h, I, J)DDS). In this paper we give a n u m b e r of c o n s t r u c t i o n s of DDS. Let
C(h,J)={Y=(xl,
x2,...,xj)lxjnonnegativeintegersand
~ xj=h}. j= 1
An (h, J)-distinct sum set (DS) is a set
A = {aj] 1
