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Short rank-metric codes and scattered subspaces
- Publication Year :
- 2023
-
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.
- Subjects :
- Computer Science - Information Theory
Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2306.01315
- Document Type :
- Working Paper