Abstract
We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets a fixed number of times. We show that the existence of such an object implies the existence of a near-resolvable design. We provide examples and general constructions of these objects, some of which lead to new parameter families of near-resolvable designs on a non-prime-power number of points. Our constructions employ cyclotomy, partial difference sets, and Galois rings.
Original language | English (US) |
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Pages (from-to) | 415-424 |
Number of pages | 10 |
Journal | Designs, Codes, and Cryptography |
Volume | 84 |
Issue number | 3 |
DOIs | |
State | Published - Sep 1 2017 |
All Science Journal Classification (ASJC) codes
- Computer Science Applications
- Applied Mathematics