Abstract
AbstractA 2-$$(v,k,\lambda )$$
(
v
,
k
,
λ
)
design is additive (or strongly additive) if it is possible to embed it in a suitable abelian group G in such a way that its block set is contained in (or coincides with) the set of all zero-sum k-subsets of its point set. Explicit results on the additivity or strong additivity of symmetric designs and subspace 2-designs are presented. In particular, the strong additivity of PG$$_d(n,q)$$
d
(
n
,
q
)
, which was known to be additive only for $$q=2$$
q
=
2
or $$d=n-1$$
d
=
n
-
1
, is always established.
Funder
Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni
Hrvatska Zaklada za Znanost
Università degli Studi di Roma La Sapienza
Publisher
Springer Science and Business Media LLC
Reference30 articles.
1. Beth T., Jungnickel D., Lenz H.: Design Theory. Cambridge University Press, Cambridge (1999).
2. Braun M., Etzion T., Östergård P.R.J., Vardy A., Wassermann A.: On the existence of $$q$$-analogs of Steiner systems. Forum of Mathematics, PI 4, (2016).
3. Braun M., Kiermaier M., Wassermann A.: $$q$$-Analogs of designs: subspace designs. In: Greferath M., Pavcevic M.O., Silberstein N., Angeles Vazquez-Castro M. (eds.) Network coding and subspace designs. Springer, Newyork (2018).
4. Bryant D., Colbourn C.J., Horsley D., Wanless I.M.: Steiner triple systems with high chromatic index. SIAM J. Discret. Math. 31, 2603–2611 (2017).
5. Bryant D., Horsley D.: A second infinite family of Steiner triple systems without almost parallel classes. J. Comb. Theory Ser. A 120, 1851–1854 (2013).