Ovoids of the non-degenerate quadric Q(4,q) of PG(4,q) have been studied since the end of the ’80s. They are rare objects and, beside the classical example given by an elliptic quadric, only three classes are known for q odd, one class for q even, and a sporadic example for q = 3^5 . It is well known that to any ovoid of Q(4,q) a bivariate polynomial f(x, y) can be associated. In this paper we classify ovoids of Q(4,q) whose correspondingpolynomial f(x, y) has “low degree” compared with q, in particular, deg(f)<(1/6.3q)^(3/13)-1. Finally, as an application, two classes of permutation polynomials in characteristic 3 are obtained.
On the Classification of Low-Degree Ovoids of Q(4,q) / Bartoli, D.; Durante, N.. - In: COMBINATORICA. - ISSN 0209-9683. - 42:S1(2022), pp. 953-969. [10.1007/s00493-022-5005-3]
On the Classification of Low-Degree Ovoids of Q(4,q)
Bartoli D.
;Durante N.
2022
Abstract
Ovoids of the non-degenerate quadric Q(4,q) of PG(4,q) have been studied since the end of the ’80s. They are rare objects and, beside the classical example given by an elliptic quadric, only three classes are known for q odd, one class for q even, and a sporadic example for q = 3^5 . It is well known that to any ovoid of Q(4,q) a bivariate polynomial f(x, y) can be associated. In this paper we classify ovoids of Q(4,q) whose correspondingpolynomial f(x, y) has “low degree” compared with q, in particular, deg(f)<(1/6.3q)^(3/13)-1. Finally, as an application, two classes of permutation polynomials in characteristic 3 are obtained.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.