The paper claims an asymptotic rate-distance tradeoff for locally repairable codes over arbitrary finite fields and arbitrary locality using local expansions at a rational place, but the construction has a critical flaw.
Aaltonen, Linear programming bounds for tree codes, IEEE Trans
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Constructive asymptotic bounds of locally repairable codes via function fields
The paper claims an asymptotic rate-distance tradeoff for locally repairable codes over arbitrary finite fields and arbitrary locality using local expansions at a rational place, but the construction has a critical flaw.