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Does anyone keep a database of (or including) linear codes with small covering radius? I'm specifically interested in the smallest-dimension codes known of covering radius R ($2\le R \le 4$ say) for each codimension (up to codimension 10 or 12) over various small fields, especially $\mathbb{F}_3$, $\mathbb{F}_5$ and maybe $\mathbb{F}_7$. There are various papers giving data for specific fields, few very recent, but no integrated dataset that I can find.

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