Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4582812 | Finite Fields and Their Applications | 2015 | 20 Pages |
Abstract
A difference system of set (DSS) is a collection of t disjoint Ïi-subsets Qi, 0â¤iâ¤tâ1, of Zn such that every non-identity element of Zn appears at least Ï times in the multiset {aâb|aâQi,bâQj,0â¤i,jâ¤tâ1,iâ j}. A DSS is regular if Ïi is constant for 0â¤iâ¤tâ1, and a DSS is perfect if every element of Zn is contained exactly Ï times in the above multiset. In this paper, we consider a collection of 3-subsets of a finite field of a prime order p=ef+1 to be a DSS. We present a condition for which the collection forms a regular DSS and give a lower bound on the parameter Ï using cyclotomic numbers for e=3,4 and 6. For the same values of e, we also show a condition for which a collection of 3-subsets is a perfect DSS.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Shoko Chisaki, Nobuko Miyamoto,