On binary constructions of quantum codes

Cohen, Gérard D.; Encheva, Sylvia B.; Litsyn, Simon

doi:10.1109/itcom.1999.781458

Cited by 9 publications

(17 citation statements)

References 11 publications

(26 reference statements)

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“…In [23], dual-containing binary codes which can be extended to a bigger code have been considered while in Corollary 11 we make no such assumption. Furthermore, in [24] it was shown that the construction provided in [23] is related to the second generalized-Hamming weights, which basically depends on the subspace property of the code, while the symbol-pair distance of the code is does not use the subspace structure and depends only on the locality properties of codewords. Hence, we feel that the two constructions are inherently different.…”

Section: B Quantum Error-correcting Codesmentioning

confidence: 99%

Quantum codes via binary codes over symbol-pair metric

Jha¹,

Parampalli²,

Singh³

2022

Preprint

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Stabilizer codes, introduced in \cite{gottesman}, \cite{GF(4)}, have been a prominent example of quantum codes constructed via classical codes. The paper \cite{GF(4)}, introduces the stabilizer formalism for obtaining additive quantum codes of length n from Hermitian self-orthogonal codes of length n over GF(4). In the present work, we present a few stabilizer code constructions considering binary codes over the symbol-pair metric (see \cite{sp}). Specifically, the present work constructs additive quantum codes of length n from certain binary codes of length n considered over the symbol-pair metric. We also present the Modified CSS Construction which is used to obtain quantum codes with parameters $[[15,$ $4,$ $3\leq d\leq7]]$, $[[31,$ $10,$ $5\leq d\leq9]]$, $[[62,$ $20,$ $5\leq d]]$, $[[63,$ $18,$ $7\leq d]]$.<br>

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Section: B Quantum Error-correcting Codesmentioning

confidence: 99%

Quantum codes via binary codes over symbol-pair metric

Jha¹,

Parampalli²,

Singh³

2022

Preprint

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“…From Lemma 3.2, there exists a cyclotomic coset containing at least two consecutive integers; here it is the coset C 8 = {8, 9, 14}. Let C be the cyclic code generated by the product of the minimal polynomials C = g(x) = M (4) (x)M (8) Proof: We know that gcd(q, n) = 1. Let C be the cyclic code generated the product of the minimal polynomials M (s) (x)M (s+2) (x) .…”

Section: Construction III -Codes Derived From Steane's Constructionmentioning

confidence: 99%

“…From Lemma 3.2, there exists a cyclotomic coset containing at least two consecutive integers; here it is the coset C 8 = {8, 9, 14}. Let C be the cyclic code generated by the product of the minimal polynomials C = g(x) = M (4) (x)M (8) ] 5 code. Theorem 3.5: Let q ≥ 3 be a prime power, n > q be a prime number and consider that m = ord n (q) ≥ 2.…”

Section: Construction III -Codes Derived From Steane's Constructionmentioning

confidence: 99%

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On the Construction of Nonbinary Quantum BCH Codes

Guardia

2014

IEEE Trans. Inform. Theory

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Four quantum code constructions generating several new families of good nonbinary quantum nonprimitive non-narrow-sense Bose-Chaudhuri-Hocquenghem (BCH) codes are presented in this paper. The first two ones are based on Calderbank-Shor-Steane (CSS) construction derived from two nonprimitive BCH codes, not necessarily self-orthogonal. The third one is based on nonbinary Steane's enlargement of CSS codes applied to suitable sub-families of nonprimitive non-narrow-sense BCH codes. The fourth construction is derived from suitable sub-families of Hermitian self-orthogonal nonprimitive non-narrow-sense BCH codes. These constructions generate new families of quantum BCH codes whose parameters are better than the ones available in the literature

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“…The several methods for constructing good families of quantum codes by numerous authors over recent years have been proposed. In [8]- [12] many binary quantum codes have been constructed by using classical error-correcting codes, such as Reed-Solomon codes, Reed-Muller codes, and algebraic-geometric codes. The theory was later extended to the nonbinary case, which authors in [13]- [15] have introduced nonbinary quantum codes for the fault-tolerant quantum computation.…”

Section: Introductionmentioning

confidence: 99%

Quantum stabilizer codes from Abelian and non-Abelian groups association schemes

Naghipour

Jafarizadeh

Shahmorad

2015

Int. J. Quantum Inform.

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A new method for the construction of the binary quantum stabilizer codes is provided, where the construction is based on Abelian and non-Abelian groups association schemes. The association schemes based on non-Abelian groups are constructed by bases for the regular representation from U 6n , T 4n , V 8n and dihedral D 2n groups. By using Abelian group association schemes followed by cyclic groups and non-Abelian group association schemes a list of binary stabilizer codes up to 40 qubits is given in tables 4, 5, and 10. Moreover, several binary stabilizer codes of distances 5 and 7 with good quantum parameters is presented. The preference of this method specially for Abelian group association schemes is that one can construct any binary quantum stabilizer code with any distance by using the commutative structure of association schemes.

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On binary constructions of quantum codes

Abstract: We improve estimates on the parameters of quantum codes obtained by Steane's construction from binary codes. This yields several new families of quantum codes.

Cited by 9 publications

References 11 publications

Quantum codes via binary codes over symbol-pair metric

Quantum codes via binary codes over symbol-pair metric

On the Construction of Nonbinary Quantum BCH Codes

Quantum stabilizer codes from Abelian and non-Abelian groups association schemes

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