Line Polar Grassmann Codes of Orthogonal Type

TL;DR

This paper determines the minimum distance of line polar Grassmann codes of orthogonal type over finite fields with odd characteristic, advancing understanding of their error-correcting capabilities.

Contribution

It provides a complete calculation of the minimum distance for these codes, which was previously unknown, enhancing their theoretical foundation.

Findings

Minimum distance fully determined for odd q

Improves understanding of code error correction

Advances the theory of orthogonal Grassmannian codes

Abstract

Polar Grassmann codes of orthogonal type have been introduced in I. Cardinali and L. Giuzzi, \emph{Codes and caps from orthogonal Grassmannians}, {Finite Fields Appl.} {\bf 24} (2013), 148-169. They are subcodes of the Grassmann code arising from the projective system defined by the Pl\"ucker embedding of a polar Grassmannian of orthogonal type. In the present paper we fully determine the minimum distance of line polar Grassmann Codes of orthogonal type for $q$ odd.