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Designs, Codes and Cryptography

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30-08-2016

Near-complete external difference families

Authors: James A. Davis, Sophie Huczynska, Gary L. Mullen

Published in: Designs, Codes and Cryptography | Issue 3/2017

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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.

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Title: Near-complete external difference families
Authors: James A. Davis
Sophie Huczynska
Gary L. Mullen
Publication date: 30-08-2016
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 3/2017
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-016-0275-7

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Near-complete external difference families

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