New quantum codes from matrix-product codes over small fields

Song, Hao; Li, Ruihu; Liu, Yang; Guo, Guanmin

doi:10.1007/s11128-020-02722-5

Cited by 6 publications

(7 citation statements)

References 24 publications

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“…Most of these papers are devoted to quantum MDS codes which have relatively small length [12,26,39]. Since we are able to construct QECCs of large length, we use two recent articles [36,11] for comparing and show that with our results we can improve the parameters of a number of codes there introduced.…”

Section: Introductionmentioning

confidence: 77%

“…QECCs were firstly introduced in the binary case which contains the seminal papers in the subject [9,22,7,8,25,3,4]. Later QECCs were studied for the general q-ary case (see [6,33,5,16,24,28,2,29,31,27,30,36,19,21,20,10,11] among many others articles). This general case is particularly interesting for fault-tolerant computing [32].…”

Section: Introductionmentioning

confidence: 99%

“…improving some codes in (and adding a new one to)[36, Table 3].Similarly, considering n = 234, we get stabilizer quantum codes over F 5 with parameters as in…”

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confidence: 99%

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On the generalization of the construction of quantum codes from Hermitian self-orthogonal codes

Galindo¹,

Hernando²

2020

Preprint

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An important strength of the q-ary stabilizer quantum codes is that they can be constructed from Hermitian self-orthogonal q 2 -ary linear codes. We prove that this result can be extended to q 2 ℓ -ary linear codes, ℓ > 1, and give a result for easily obtaining codes of the last type. As a consequence we provide several new binary stabilizer quantum codes which are records according to [23] and new 2 = q-ary ones improving others in the literature.

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Section: Introductionmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

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On the generalization of the construction of quantum codes from Hermitian self-orthogonal codes

Galindo¹,

Hernando²

2020

Preprint

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“…QECCs were firstly introduced in the binary case, where one finds the seminal papers on the subject [4,5,[7][8][9]21,24]. Later QECCs were studied for the general q-ary case (see [1,3,6,11,12,[16][17][18][19][20]25,27,28,[30][31][32]35,39] among many other articles). The general case is particularly interesting for fault-tolerant computing [10,22,29,33,36,37,41].…”

Section: Introductionmentioning

confidence: 99%

“…Most of these papers are devoted to quantum MDS codes which have relatively small length [13,26,43]. Since we are able to construct long QECCs, we use recent articles [12,34,39] for comparison and show that with our method we can improve the parameters of a number of codes therein.…”

Section: Introductionmentioning

confidence: 99%

On the generalization of the construction of quantum codes from Hermitian self-orthogonal codes

Galindo

Hernando

2022

Des. Codes Cryptogr.

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Many q-ary stabilizer quantum codes can be constructed from Hermitian self-orthogonal $$q^2$$ q 2 -ary linear codes. This result can be generalized to $$q^{2 m}$$ q 2 m -ary linear codes, $$m > 1$$ m > 1 . We give a result for easily obtaining quantum codes from that generalization. As a consequence we provide several new binary stabilizer quantum codes which are records according to Grassl (Bounds on the minimum distance of linear codes, http://www.codetables.de, 2020) and new q-ary ones, with $$q \ne 2$$ q ≠ 2 , improving others in the literature.

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