Year: 2025
Type: preprint
Abstract: An $\mathbb{F}_q$-linear code of minimum distance $d$ is called complete if it is not contained in a larger $\mathbb{F}_q$-linear code of minimum distance $d$. In this paper, we classify $\mathbb{F}_q$-linear complete symmetric rank-distance (CSRD) codes in $M_{3\times 3}(\mathbb{F}_q)$ up to equivalence. This includes the classification of $\mathbb{F}_q$-linear maximum symmetric rank-distance (MSRD) codes in $M_{3\times 3}(\mathbb{F}_q)$. Our approach is mainly geometric, and our results contribute towards the classification of nets of conics in $\mathrm{PG}(2, q)$.
Source: arXiv (Cornell University)
Authors: Alnajjarine, Nour, Lavrauw, Michel
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979268763
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