On the Sparseness of Certain MRD Codes

06/27/2019

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by   Heide Gluesing-Luerssen, et al.

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We determine the proportion of [3× 3;3]-MRD codes over F_q within the space of all 3-dimensional rank-metric codes over the same field. This shows that these MRD codes are sparse in the sense that this proportion tends to 0 as q→∞. 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.