Circular external difference families, graceful labellings and cyclotomy

Paterson, Maura B. and Stinson, D.R. (2024) Circular external difference families, graceful labellings and cyclotomy. Discrete Mathematics 347 (10), p. 114103. ISSN 0012-365X.

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Official URL: https://doi.org/10.1016/j.disc.2024.114103

Abstract

(Strong) circular external difference families (which we denote as CEDFs and SCEDFs) can be used to construct nonmalleable threshold schemes. They are a variation of (strong) external difference families, which have been extensively studied in recent years. We provide a variety of constructions for CEDFs based on graceful labellings (α-valuations) of lexicographic products Cn · K^c_ℓ, where C_n denotes a cycle of length n. SCEDFs having more than two subsets do not exist. However, we can construct close approximations (more specifically, certain types of circular algebraic manipulation detection (AMD) codes) using the theory of cyclotomic numbers in finite fields.

Metadata

Item Type:	Article
School:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Maura Paterson
Date Deposited:	24 May 2024 15:51
Last Modified:	16 Jun 2024 15:56
URI:	https://eprints.bbk.ac.uk/id/eprint/53573

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