Abstract
Entanglement-assisted quantum error correcting code (EAQECC) is a generalization of standard stabilizer quantum code. Maximal entanglement EAQECCs can achieve the EA-hashing bound asymptotically. In this work, we give elementary recursive constructions of quaternary zero radical codes with dual distance three for all n ≥ 4. Consequently, good maximal entanglement EAQECCs of minimum distance three for such length n are obtained. Almost all of these EAQECCs are optimal or near optimal according to the EA-quantum Hamming bound.
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