 Author
 Bart De Bruyn (UGent)
 Organization
 Abstract
 A twocharacter set is a set of points of a finite projective space that has two intersection numbers with respect to hyperplanes. Twocharacter sets are related to strongly regular graphs and twoweight codes. In the literature, there are plenty of constructions for (nontrivial) twocharacter sets by considering suitable subsets of quadrics and Hermitian varieties. Such constructions exist for the quadrics Q(+)(2n1, q) subset of PG(2n  1, q), Q()(2n + 1, q) subset of PG(2n + 1, q) and the Hermitian varieties H(2n  1, q(2)) subset of PG(2n  1, q(2)), H(2n, q(2)) subset of PG(2n, q2). In this note we show that every twocharacter set of PG(2n, q) that is contained in a given nonsingular parabolic quadric Q(2n, q) subset of PG(2n, q) is a subspace of PG(2n, q). This offers some explanation for the absence of the parabolic quadrics in the above mentioned constructions.
 Keywords
 Twocharacter set, parabolic quadric, STRONGLY REGULAR GRAPHS, POLAR SPACES, MSYSTEMS, 2WEIGHT CODES, TIGHT SETS, MOVOIDS, GEOMETRY, CAMERON, LIEBLER, Q)
Downloads

(...).pdf
 full text
 
 UGent only
 
 
 137.62 KB
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU8510640
 Chicago
 De Bruyn, Bart. 2016. “Twocharacter Sets as Subsets of Parabolic Quadrics.” Ars Combinatoria 127: 125–132.
 APA
 De Bruyn, B. (2016). Twocharacter sets as subsets of parabolic quadrics. ARS COMBINATORIA, 127, 125–132.
 Vancouver
 1.De Bruyn B. Twocharacter sets as subsets of parabolic quadrics. ARS COMBINATORIA. 2016;127:125–32.
 MLA
 De Bruyn, Bart. “Twocharacter Sets as Subsets of Parabolic Quadrics.” ARS COMBINATORIA 127 (2016): 125–132. Print.
@article{8510640, abstract = {A twocharacter set is a set of points of a finite projective space that has two intersection numbers with respect to hyperplanes. Twocharacter sets are related to strongly regular graphs and twoweight codes. In the literature, there are plenty of constructions for (nontrivial) twocharacter sets by considering suitable subsets of quadrics and Hermitian varieties. Such constructions exist for the quadrics Q(+)(2n1, q) subset of PG(2n  1, q), Q()(2n + 1, q) subset of PG(2n + 1, q) and the Hermitian varieties H(2n  1, q(2)) subset of PG(2n  1, q(2)), H(2n, q(2)) subset of PG(2n, q2). In this note we show that every twocharacter set of PG(2n, q) that is contained in a given nonsingular parabolic quadric Q(2n, q) subset of PG(2n, q) is a subspace of PG(2n, q). This offers some explanation for the absence of the parabolic quadrics in the above mentioned constructions.}, author = {De Bruyn, Bart}, issn = {03817032}, journal = {ARS COMBINATORIA}, language = {eng}, pages = {125132}, title = {Twocharacter sets as subsets of parabolic quadrics}, volume = {127}, year = {2016}, }