Difference systems of sets and cyclotomy

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Difference systems of sets (DSS) are combinatorial configurations that arise in connection with code synchronization. A method for the construction of DSS from partitions of cyclic difference sets was introduced in [V.D. Tonchev, Difference systems of sets and code synchronization, Rend. Sem. Mat. Messina, Ser. II, t. XXV 9 (2003) 217–226] and applied to cyclic difference sets (n, (n−1)/2, (n−3)/4) of Paley type, where n ≡ 3(mod 4) is a prime number. This paper develops similar constructions for prime numbers n ≡ 1(mod 4) that use partitions of the set of quadratic residues, as well as more general cyclotomic classes.

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Copyright © 2007 Elsevier B.V. All rights reserved. Publisher’s version of record: https://doi.org/10.1016/j.disc.2007.08.017

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Discrete Mathematics