A characterization of \(\mathbb F_q\)-linear subsets of affine spaces \(\mathbb F_{q^2}^n\)

  • Edoardo Ballico Department of Mathematics, University of Trento, 38123 Povo (TN), Italy.
Keywords: Finite field, Hermitian form

Abstract

Let \(q\) be an odd prime power. We discuss possible definitions over \(\mathbb F_{q^2}\) (using the Hermitian form) of circles, unit segments and half-lines. If we use our unit segments to define the convex hulls of a set \(S\subset \mathbb F_{q^2}^n\) for \(q\notin \{3,5,9\}\) we just get the \(\mathbb F_q\)-affine span of \(S\).

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Published
2022-04-04
How to Cite
[1]
E. Ballico, “A characterization of \(\mathbb F_q\)-linear subsets of affine spaces \(\mathbb F_{q^2}^n\)”, CUBO, vol. 24, no. 1, pp. 95–103, Apr. 2022.
Section
Articles