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arXiv · 1412.5466

Enumerative Coding for Line Polar Grassmannians with applications to codes

Ilaria Cardinali·Luca Giuzzi
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Abstract

A $k$-polar Grassmannian is the geometry having as pointset the set of all $k$-dimensional subspaces of a vector space $V$ which are totally isotropic for a given non-degenerate bilinear form $μ$ defined on $V.$ Hence it can be regarded as a subgeometry of the ordinary $k$-Grassmannian. In this paper we deal with orthogonal line Grassmannians and with symplectic line Grassmannians, i.e. we assume $k=2$ and $μ$ a non-degenerate symmetric or alternating form. We will provide a method to efficiently enumerate the pointsets of both orthogonal and symplectic line Grassmannians. This has several nice applications; among them, we shall discuss an efficient encoding/decoding/error correction strategy for line polar Grassmann codes of both types.

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Ilaria Cardinali, Luca Giuzzi. 2018-04-10. Enumerative Coding for Line Polar Grassmannians with applications to codes. https://doi.org/10.1016/j.ffa.2017.03.005

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