Abstract
Let G be an additive group and C k be the additive group of the ring Z k of residues modulo k. If there exist a (G, k, λ) difference family and a (G, k, λ) perfect Mendelsohn difference family, then there also exists a \((C_k \oplus G,k,\lambda )\) difference family. If the (G, k, λ) difference family and the (G, k, λ) perfect Mendelsohn difference family are further compatible, then the resultant \((C_k \oplus G,k,\lambda )\) difference family is elementary resolvable. By first constructing several series of perfect Mendelsohn difference families, many \((C_k \oplus G,k,\lambda )\) difference families and elementary resolvable \((C_k \oplus G,k,\lambda )\) difference families are thus obtained.
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Lam, C., Miao, Y. \((C_k \oplus G,k,\lambda )\) Difference Families. Designs, Codes and Cryptography 24, 291–304 (2001). https://doi.org/10.1023/A:1011275205253
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DOI: https://doi.org/10.1023/A:1011275205253