On MDS linear complementary dual codes and entanglement-assisted quantum codes

Qian, Jianfa; Zhang, Lina

doi:10.1007/s10623-017-0413-x

Cited by 83 publications

(34 citation statements)

References 23 publications

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“…Recently, one can find in the literature some papers where the above formula (or formulae derived from it) are used for determining the entanglement corresponding to EAQECCs over arbitrary finite fields (see, for instance [6,9,17,21]). Although it holds for any finite field, we have found no proof in the literature and, thus, this work fills this gap.…”

Section: Introductionmentioning

confidence: 99%

Entanglement-assisted quantum error-correcting codes over arbitrary finite fields

Galindo

Hernando

Matsumoto

et al. 2019

Quantum Inf Process

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We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as well. We also give a Gilbert-Varshamov bound for EAQECCs and constructions of EAQECCs coming from punctured self-orthogonal linear codes which are valid for any finite field.2010 Mathematics Subject Classification. 81P70; 94B65; 94B05.

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Section: Introductionmentioning

confidence: 99%

Entanglement-assisted quantum error-correcting codes over arbitrary finite fields

Galindo

Hernando

Matsumoto

et al. 2019

Quantum Inf Process

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“…Several articles have explored the construction of EAQECCs from classical linear codes as binary BCH codes [8,18,21], constacyclic codes [17,27], constacyclic LCD codes [24], cyclic codes [25], generalized Reed-Solomon codes [14,19,20], negacyclic BCH codes [6,7] and algebraic-geometry codes [23]. These papers address particular cases and determine their parameters but no general formula for the parameters of EAQECCs using the previous families of codes is known.…”

Section: Introductionmentioning

confidence: 99%

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

Galindo

Hernando

Ruano

2021

Quantum Inf Process

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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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“…In [14], we introduced the so-called k-Galois LCD codes which include the usual LCD codes and Hermitian LCD codes as two special cases, and gave sufficient and necessary conditions for a code to be a k-Galois LCD code. Recently, Qian, Zhang [15], and Guenda, Jitman, Gulliver [16] exhibited an application of LCD codes in constructing good EAQECCs.…”

Section: Introductionmentioning

confidence: 99%