A design is G-additive, with G an abelian group, if its points are in G and each block is zero-sum in G. All the few known “manageable” additive Steiner 2-designs are EA(q)-additive for a suitable q, where EA(q) is the elementary abelian group of order q. We present some general constructions for EA(q)-additive Steiner 2-designs which unify the known ones and allow to find a few new ones: an EA(28)-additive 2-(52, 4, 1) design which is also resolvable, and three pairwise non-isomorphic EA(35)-additive 2-(121, 4, 1) designs, none of which is the point-line design of PG(4,3). In the attempt to find also an EA(29)-additive 2-(511, 7, 1) design, we prove that a putative (subspace) 2-analog of a 2-(9, 3, 1) design cannot be cyclic.
EA(q)-additive Steiner 2-designs
Galici M.;Montinaro A.;
2026-01-01
Abstract
A design is G-additive, with G an abelian group, if its points are in G and each block is zero-sum in G. All the few known “manageable” additive Steiner 2-designs are EA(q)-additive for a suitable q, where EA(q) is the elementary abelian group of order q. We present some general constructions for EA(q)-additive Steiner 2-designs which unify the known ones and allow to find a few new ones: an EA(28)-additive 2-(52, 4, 1) design which is also resolvable, and three pairwise non-isomorphic EA(35)-additive 2-(121, 4, 1) designs, none of which is the point-line design of PG(4,3). In the attempt to find also an EA(29)-additive 2-(511, 7, 1) design, we prove that a putative (subspace) 2-analog of a 2-(9, 3, 1) design cannot be cyclic.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
