It is known that the Hermitian varieties are codewords in the code dened bythe points and hyperplanes of the projective spaces PG(r; q2). In nite geometry,also quasi-Hermitian varieties are dened. These are sets of points of PG(r; q2) ofthe same size as a non-singular Hermitian variety of PG(r; q2), having the sameintersection sizes with the hyperplanes of PG(r; q2). In the planar case, this reducesto the denition of a unital. A famous result of Blokhuis, Brouwer, and Wilbrinkstates that every unital in the code of the points and lines of PG(2; q2) is a Hermitiancurve. We prove a similar result for the quasi-Hermitian varieties in PG(3; q2),q=ph, as well as in PG(r; q2),q=pprime, orq=p2,pprime, andr>4
A characterization of Hermitianvarieties as codewords
Angela Aguglia;Daniele Bartoli
;
2018
Abstract
It is known that the Hermitian varieties are codewords in the code dened bythe points and hyperplanes of the projective spaces PG(r; q2). In nite geometry,also quasi-Hermitian varieties are dened. These are sets of points of PG(r; q2) ofthe same size as a non-singular Hermitian variety of PG(r; q2), having the sameintersection sizes with the hyperplanes of PG(r; q2). In the planar case, this reducesto the denition of a unital. A famous result of Blokhuis, Brouwer, and Wilbrinkstates that every unital in the code of the points and lines of PG(2; q2) is a Hermitiancurve. We prove a similar result for the quasi-Hermitian varieties in PG(3; q2),q=ph, as well as in PG(r; q2),q=pprime, orq=p2,pprime, andr>4I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
