Near-complete external difference families
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.
Citation
Davis , J A , Huczynska , S & Mullen , G L 2017 , ' Near-complete external difference families ' , Designs, Codes and Cryptography , vol. 84 , no. 3 , pp. 415-424 . https://doi.org/10.1007/s10623-016-0275-7
Publication
Designs, Codes and Cryptography
Status
Peer reviewed
ISSN
0925-1022Type
Journal article
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.