Design theory
Recursive constructions for cyclic BIB designs and their generalizations
Discrete Mathematics
Constructions of (q,k,1) difference families with q a prime power and k=4,5
Selected papers of the 14th British conference on Combinatorial conference
A powerful method for constructing difference families and optimal optical orthogonal codes
Designs, Codes and Cryptography
From a (G, k, 1) to a (Ck ⊕ G, k, 1) Difference Family
Designs, Codes and Cryptography
(C_k \oplus G, k, \lambda) Difference Families
Designs, Codes and Cryptography
Some progress on (v, 4, 1) difference families and optical orthogonal codes
Journal of Combinatorial Theory Series A
Note: A cyclic group action on resolutions of quadruple systems
Journal of Combinatorial Theory Series A
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A Steiner 2-design is said to be G-invariantly resolvable if admitsan automorphism group G and a resolution invariantunder G. Introducing and studying resolvable differencefamilies, we characterize the class of G-invariantlyresolvable Steiner 2-designs arising from relative differencefamilies over G. Such designs have been alreadystudied by Genma, Jimbo, and Mishima [13] in the case in whichG is cyclic. Developping their results, we provethat any (p, k, 1)-DF (p prime) whosebase blocks exactly cover p−1/k(k−1) distinctcosets of the k-th roots of unity (mod p),leads to a Ckp-invariantly resolvable cyclic(kp,k,1)-BBD. This induced us to propose severalconstructions for DF‘s having this property. In such a way weprove, in particular, the existence of a C5p-invariantlyresolvable cyclic (5p, 5, 1)-BBD for each prime p= 20n + 1