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Consider encoding a qubit into $n$ qubits. It is well known that the smallest error detecting code is in $n=4$ qubits and the smallest error correcting code is in $n=5$ qubits.

Is there a similar result for qudits? If we encode a qudit into $n$ qudits, are there any results on the smallest $n$ we need in order to detect or correct a single qudit error?

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