Short rank-metric codes and scattered subspaces

Stefano Lia; Giovanni Longobardi; Giuseppe Marino; Rocco Trombetti

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arXiv · 2306.01315

Short rank-metric codes and scattered subspaces

Stefano Lia·Giovanni Longobardi·Giuseppe Marino·Rocco Trombetti

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Abstract

By exploiting the connection between scattered $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}^3$ and minimal non degenerate $3$-dimensional rank metric codes of $\mathbb{F}_{q^m}^{n}$, $n \geq m+2$, described in [2], we will exhibit a new class of codes with parameters $[m+2,3,m-2]_{q^m/q}$ for infinite values of $q$ and $m \geq 5$ odd. Moreover, by studying the geometric structures of these scattered subspaces, we determine the rank weight distribution of the associated codes.

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Stefano Lia, Giovanni Longobardi, Giuseppe Marino, Rocco Trombetti. 2023-06-02. Short rank-metric codes and scattered subspaces. https://arxiv.org/abs/2306.01315

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