New families of semi-regular relative difference sets by James Arthur Davis

Cover of: New families of semi-regular relative difference sets | James Arthur Davis

Published by Hewlett-Packard Laboratories, Technical Publications Dept. in Palo Alto, Calif .

Written in English

Read online

Subjects:

  • Difference sets,
  • Combinatorial analysis

Edition Notes

Book details

StatementJames A. Davis.
SeriesHP Laboratories technical report -- HPL-96-34.
ContributionsJedwab, Jonathan., Mowbray, Miranda., Hewlett-Packard Laboratories.
The Physical Object
Pagination16 p. ;
Number of Pages16
ID Numbers
Open LibraryOL17597989M
OCLC/WorldCa43946897

Download New families of semi-regular relative difference sets

We recursively construct a new family New families of semi-regular relative difference sets book (26d+4, 8, 26d+4, 26d+1) semi-regular relative difference sets in abelian groups G relative to an elementary abelian subgroup U.

New Families of Semi-Regular Relative Difference Sets. We give two constructions for semi-regular relative difference sets (RDSs) in groups whose order is not a prime power, where the order u of the forbidden subgroup is greater than 2. No such RDSs were previously known.

We use examples from the first construction to produce semi-regular RDSs in groups whose order can contain more than two distinct prime by: CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We give two constructions for semi-regular relative difference sets (RDSs) in groups whose order is not a prime power, where the order u of the forbidden subgroup is greater than 2.

No such RDSs were previously known. We use examples from the first construction to produce semi-regular RDSs in groups whose. New families of semi-regular relative difference sets.

By J. Davis, J Jedwab and Bristol (United Kingdom) Hewlett-Packard Laboratories. Abstract. SIGLEAvailable from British Library Document Supply Centre-DSC(HPL(rev.1)) / BLDSC. We recursively construct a new family of (26d+4, 8, 26d+4, 26d+1) semi-regular relative difference sets in abelian groups G relative to an elementary abelian subgroup U.

The initial case d = 0 of the recursion comprises examples of (16, 8, 16, 2) relative difference sets for four distinct pairs (G, U). New families of semi-regularrelative difference sets James A. Davis; Mathematics and Computer Science, University of Richmond, VirginiaU.S.A.

In this note, we shall construct a new family of relative difference sets by generalizing a result of Spence [8]. THEOREM. Let q be a prime power, d a positive integer, N = EA(gd + 1) the elementary abelian group of order qd + 1, and K any group of order " The author thanks the University of Waterloo for its hospitality during the time of this.

Abstract. We recursively construct a new family of (2 6d+4, 8, 2 6d+4, 2 6d+1) semi-regular relative difference sets in abelian groups G relative to an elementary abelian subgroup initial case d = 0 of the recursion comprises examples of (16, 8, 16, 2) relative difference sets for.

building sets, characters We recursively construct a new family of (26d+4, 8, 26d+4, 26d+1) semi-regular relative difference sets in abelian groupsG relative to an elementary abelian subgroupU.

The initial case d = 0 of the recursion comprises examples New families of semi-regular relative difference sets book (16,8,16,2) relative difference sets for four distinct pairs (G, U). As nouns the difference between family and relative is that family is (lb) a group of people who are closely related to one another (by blood or marriage); for example, a set of parents and their children; an immediate family while relative is someone in the same family; someone connected by blood, marriage, or adoption.

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In fact one difference set was omitted. Thus the above construction gives three inequivalent (35, 15, 6) difference sets in Zs x ZF and four inequivalent (36, 15, 6) difference sets in Z;3 x_ Z, x Z, which are the only ones possible.

REFERENCES 1. MCFARLAND, A family of difference sets in non-cyclic groups, J. Combinatorial Theory Lingadapted from UMass LingPartee lecture notes March 1, p.

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