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تسجيل مستخدم جديدOn the Sparseness of Certain MRD Codes
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نشر من قبل
Heide Gluesing-Luerssen
تاريخ النشر
2019
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الهندسة المعلوماتية
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English
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Heide Gluesing-Luerssen
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We determine the proportion of $[3times 3;3]$-MRD codes over ${mathbb F}_q$ within the space of all $3$-dimensional $3times3$-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 $qrightarrowinfty$. 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.
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