Abstract
Given a subgroup N of an additive group G, a (G,N,k,1) difference family (DF) is a set D of k-subsets of G such that (d − d′ | d, d′ ∈ D, d ≠ d′, D ∈ D) = G − N. Generalizing a construction by Genma, Jimbo, and Mishima [4], we give a new condition for realizing a (Ck ⊕ G, Ck × {0}, k, 1)-DF starting from a (G, {0}, k, 1)-DF. Among the consequences, new cyclic Steiner 2-designs are obtained.
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Buratti, M. From a (G, k, 1) to a (Ck ⊕ G, k, 1) Difference Family. Designs, Codes and Cryptography 11, 5–9 (1997). https://doi.org/10.1023/A:1008246707730
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DOI: https://doi.org/10.1023/A:1008246707730