Order-(t-1) Balanced Multiple-Valued Filing Scheme Using Difference Vectors

A balanced multiple-valued filing scheme of order (t 1) is constructed based on the finite projective geometry PG(t, q), (t + 1) not prime, t odd. The attributes and attribute values are defined using a spread of flats from PG(t, q) as in Yamamoto etal. (Inform. Contr. 21 (1972), 72-91) and Berman (Inform. Contr. 32 (1976), 128-138). Certain structural properties of PG(t,q) are exploited, resulting in an easily constructed bucket structure. The ( t 2)-flats, which represent the buckets, are partitioned into orbits each of which is uniquely identifiable by its difference vector. The storage and retrieval algorithms are based on these difference vectors. There is no scanning of buckets or sub-buckets. The concepts in this paper are illustrated by an example based on PG(5, 2).