In this paper we investigate linear error correcting codes and projective caps related to the Grassmann embedding $\varepsilon_k^{gr}$ of an orthogonal Grassmannian $\Delta_k$. In particular, we determine some of the parameters of the codes arising from the projective system determined by $\varepsilon_k^{gr}(\Delta_k)$. We also study special sets of points of $\Delta_k$ which are met by any line of $\Delta_k$ in at most $2$ points and we show that their image under the Grassmann embedding $\varepsilon_k^{gr}$ is a projective cap.

Cardinali, I., Giuzzi, L. (2013). Codes and caps from orthogonal Grassmannians. FINITE FIELDS AND THEIR APPLICATIONS, 24, 148-169 [10.1016/j.ffa.2013.07.003].

### Codes and caps from orthogonal Grassmannians

#### Abstract

In this paper we investigate linear error correcting codes and projective caps related to the Grassmann embedding $\varepsilon_k^{gr}$ of an orthogonal Grassmannian $\Delta_k$. In particular, we determine some of the parameters of the codes arising from the projective system determined by $\varepsilon_k^{gr}(\Delta_k)$. We also study special sets of points of $\Delta_k$ which are met by any line of $\Delta_k$ in at most $2$ points and we show that their image under the Grassmann embedding $\varepsilon_k^{gr}$ is a projective cap.
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2013
Cardinali, I., Giuzzi, L. (2013). Codes and caps from orthogonal Grassmannians. FINITE FIELDS AND THEIR APPLICATIONS, 24, 148-169 [10.1016/j.ffa.2013.07.003].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/45495