Design of a Balanced Multiple-Valued Filing Scheme of Order Two Based on Cyclically Generated Spread in Finite Projective Geometry

The balanced multiple-valued filing scheme was defined by Ghosh and Abraham (1968). They constructed there two types of balanced multiplevalued filing scheme of order two. One scheme was obtained by deleting a spread generated by parallel lines in a finite affine geometry EG(t, s) and the other was obtained by deleting a partial spread generated by all the lines in a finite projective geometry PG(t, s) which have one particular point in common. The idea of these methods of construction was generalized by Koch (1967). In this paper, we shall give a new type of balanced multiple-valued filing scheme of order two constructed by deleting a cyclically generated spread in a finite t-dimensional projective geometry PG(t, s) where t + 1 is not prime. Since the spread identified with the set of attributes and the lines identified with the buckets can be generated cyclically in multiplicative representation of the points in PG(t, s), the proposed scheme can be implemented easily.