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Entanglement-assisted quantum error-correcting codes from RS codes and BCH codes with extension degree 2

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Abstract

Entanglement-assisted quantum error-correcting codes (EAQECCs) constructed from Reed–Solomon codes and BCH codes are considered in this work. It is provided a complete and explicit formula for the parameters of EAQECCs coming from any Reed–Solomon code, for the Hermitian metric, and from any BCH code with extension degree 2 and consecutive cyclotomic cosets, for both the Euclidean and the Hermitian metric. The main task in this work is the computation of a completely general formula for c, the minimum number of required maximally entangled quantum states.

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Correspondence to Diego Ruano.

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This work was supported in part by the Spanish Grants PGC2018-096446-BC21, PGC2018-096446-B-C22 and RED2018-102583-T (MCI/AEI/FEDER, UE), by the Spanish MINECO Grant RYC-2016-20208 (AEI/FSE/UE), by the Junta de CyL (Spain) Grant VA166G18, by the Generalitat Valenciana (Spain) Grant AICO- 2019-223 and by Universitat Jaume I Grant P1-1B2018-10.

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Galindo, C., Hernando, F. & Ruano, D. Entanglement-assisted quantum error-correcting codes from RS codes and BCH codes with extension degree 2. Quantum Inf Process 20, 158 (2021). https://doi.org/10.1007/s11128-021-03101-4

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