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The entanglement-assisted (EA) formalism is a generalization of the standard stabilizer formalism, and it can transform classical linear quaternary codes into entanglement-assisted quantum error correcting codes (EAQECCs) by using of shared entangled qubits between the sender and the receiver. In this work, we give elementary recursive constructions of special quaternary codes of length n and dual distance four that constructed from known caps in projective space PG(5,4) and PG(6,4) for all length 6n283. Consequently, good maximal entanglement EAQECCs of minimum distance four for such length n are constructed from the obtained quaternary codes. Index Terms - EAQECCs, maximal entanglement, quaternary code, cap.

Entanglement-assisted Quantum Codes of Distance Four Constructed from Caps in PG(5,4) and PG(6,4)