Abstract
AbstractRecently, in Innamorati and Zuanni (J. Geom 111:45, 2020. 10.1007/s00022-020-00557-0) the authors give a characterization of a Baer cone of $$\mathrm {PG}(3, q^2)$$
PG
(
3
,
q
2
)
, q a prime power, as a subset of points of the projective space intersected by any line in at least one point and by every plane in $$q^2+1$$
q
2
+
1
, $$q^2+q+1$$
q
2
+
q
+
1
or $$q^3+q^2+1$$
q
3
+
q
2
+
1
points. In this paper, we show that a similar characterization holds even without assuming that the order of the projective space is a square, and weakening the assumptions on the three intersection numbers with respect to the planes.
Funder
Università degli Studi della Campania Luigi Vanvitelli
Publisher
Springer Science and Business Media LLC
Reference7 articles.
1. Calderbank, R., Kantor, W.M.: The geometry of two-weight codes. Bull. Lond. Math. Soc. 18(2), 97–122 (1986)
2. Delsarte, P.: Two-weight linear codes and strongly regular graphs. Report R160, MBLE Res. Lab., Brussels (1971)
3. Innamorati, S., Zuanni, F.: A combinatorial characterization of the Baer and the unital cone in $${\rm PG}(3, q^2)$$. J. Geom. 111, 45 (2020). https://doi.org/10.1007/s00022-020-00557-0.
4. Napolitano, V., Zullo, F.: Codes with few weights arising from linear sets. Adv. Math. Commun. (2020). https://doi.org/10.3934/amc.2020129.
5. Napolitano, V.: On quasi-Hermitian varieties in $${\rm PG}(3, q^2)$$. Discrete Math. 339, 511–514 (2016)