Codes and caps from orthogonal Grassmannians

Abstract

In this paper we investigate linear error correcting codes and projective caps related to the Grassmann embedding ${\epsilon }_k^{gr}$ of an orthogonal Grassmannian ${\Delta }_k$. In particular, we determine some of the parameters of the codes arising from the projective system determined by ${\epsilon }_k^{gr}({\Delta }_k)$. 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 ${\epsilon }_k^{gr}$ is a projective cap.

Keywords: Polar Grassmannian; dual polar space; embedding; error correcting code; cap; Hadamard matrix; Sylvester construction (this is a slightly revised version of v2, with updated bibliography)

References in corpus (2)

• Decomposable Subspaces, Linear Sections of Grassmann Varieties, and Higher Weights of Grassmann Codes
• LDPC codes from Singer cycles

Cited by in corpus (8)

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• Line Hermitian Grassmann Codes and their Parameters
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• Intersections of the Hermitian surface with irreducible quadrics in $PG(3,q^2)$, $q$ odd
• Implementing Line-Hermitian Grassmann codes
• Polar Grassmannians and their Codes
• Affine Hermitian Grassmann Codes