Near-complete external difference families

James A. Davis; Sophie Huczynska; Gary L. Mullen

doi:10.1007/s10623-016-0275-7

Near-complete external difference families

James A. Davis^*, Sophie Huczynska, Gary L. Mullen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	415-424
Number of pages	10
Journal	Designs, Codes and Cryptography
Volume	84
Issue number	3
Early online date	30 Aug 2016
DOIs	https://doi.org/10.1007/s10623-016-0275-7
Publication status	Published - Sept 2017

Keywords

Difference family
Galois rings
Partial difference sets

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10.1007/s10623-016-0275-7

Davis_2016_Near-complete_DCC_AAM
© 2016, Springer. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at link.springer.com / https://doi.org/10.1007/s10623-016-0275-7
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Cite this

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AB - 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.

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Near-complete external difference families

Abstract

Keywords

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