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Designs, Codes and Cryptography

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02-01-2019

Almost designs and their links with balanced incomplete block designs

Authors: Jerod Michel, Qi Wang

Published in: Designs, Codes and Cryptography | Issue 9/2019

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Abstract

Almost designs (t-adesigns) were proposed and discussed by Ding as a certain generalization of combinatorial designs related to almost difference sets. Unlike t-designs, it is not clear whether t-adesigns need also be $(t-1)$-designs or $(t-1)$-adesigns. In this paper we discuss a particular class of 3-adesigns, i.e., 3-adesigns coming from certain strongly regular graphs and tournaments, and find that these are also 2-designs. We construct several classes of these, and discuss some of the restrictions on the parameters of such a class. We also construct several new classes of 2-adesigns, and discuss some of their properties as well.

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Title: Almost designs and their links with balanced incomplete block designs
Authors: Jerod Michel
Qi Wang
Publication date: 02-01-2019
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 9/2019
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-018-00596-4

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