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Two new families of entanglement-assisted quantum MDS codes from generalized Reed-Solomon codes. (English) Zbl 1417.81109

Summary: Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC by any classical linear code. In this paper, we propose two constructions of generalized Reed-Solomon codes and calculate the dimension of their hulls. With these generalized Reed-Solomon codes, we present two new infinite families of EAQECCs, which are optimal with respect to the Singleton bound for EAQECCs. Notably, the parameters of our EAQECCs are new and flexible.

MSC:

81P70 Quantum coding (general)
94B60 Other types of codes
94B05 Linear codes (general theory)
94B15 Cyclic codes
81P68 Quantum computation
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
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