On the Sparseness of Certain MRD Codes
(1906.11691)Abstract
We determine the proportion of $[3\times 3;3]$-MRD codes over ${\mathbb F}_q$ within the space of all $3$-dimensional $3\times3$-rank-metric codes over the same field. This shows that for these parameters MRD codes are sparse in the sense that the proportion tends to $0$ as $q\rightarrow\infty$. This is so far the only parameter case for which MRD codes are known to be sparse. The computation is accomplished by reducing the space of all such rank-metric codes to a space of specific bases and subsequently making use of a result by Menichetti (1973) on 3-dimensional semifields.
We're not able to analyze this paper right now due to high demand.
Please check back later (sorry!).
Generate a summary of this paper on our Pro plan:
We ran into a problem analyzing this paper.