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

Naghipour, Avaz; Jafarizadeh, M. A.; Shahmorad, S.

doi:10.1142/s0219749915500215

Cited by 9 publications

(3 citation statements)

References 44 publications

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“…Li et al [17] introduced a large number of good binary quantum codes of minimum distances five and six by Steane's Construction. In [18] good binary quantum stabilizer codes obtained via graphs of Abelian and non-Abelian groups schemes. In [19], Qian presented a new method for constructing quantum codes from cyclic codes over finite ring F 2 + vF 2 .…”

Section: Introductionmentioning

confidence: 99%

Classes of quantum codes derived from self-dual orientable embeddings of complete multipartite graphs

Naghipour

Jafarizadeh

2017

Quantum Inf Process

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This paper presents four new classes of binary quantum codes with minimum distance 3 and 4, namely Class-I, Class-II, Class-III and Class-IV. The classes Class-I and Class-II are constructed based on self-dual orientable embeddings of the complete graphs K 4r+1 and K 4s and by current graphs and rotation schemes. The parameters of two classes of quantum codes are [[2r(4r + 1), 2r(4r − 3), 3]] and [[2s(4s−1), 2(s−1)(4s−1), 3]] respectively, where r ≥ 1 and s ≥ 2. For these quantum codes, the code rate approaches 1 as r and s tend to infinity. The Class-III with rate 1 2 and with minimum distance 4 is constructed by using self-dual embeddings of complete bipartite graphs. The parameters of this class are [[rs, (r−2)(s−2) 2, 4]], where r and s are both divisible by 4. The proposed Class-IV is of minimum distance 3 and code length n = (2r+1)s 2 . This class is constructed based on self-dual embeddings of complete tripartite graph Krs,s,s and its parameters are [[(2r+1)s 2 , (rs−2)(s−1), 3]], where r ≥ 2 and s ≥ 2.

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Section: Introductionmentioning

confidence: 99%

Classes of quantum codes derived from self-dual orientable embeddings of complete multipartite graphs

Naghipour

Jafarizadeh

2017

Quantum Inf Process

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“…Li et al [17] were given a large number of good binary quantum codes of minimum distances five and six by Steane's Construction. In [18] good binary quantum stabilizer codes are obtained via graphs of Abelian and non-Abelian groups schemes. In [19], Qian presented a new method of constructing quantum codes from cyclic codes over finite ring F 2 + vF 2 .…”

Section: Introductionmentioning

confidence: 99%

“…After finding the matrices H X and H Z using the Theorems in Section 4, the code with parameters [ [18,2,3]] is obtained. Note that the matrix H Z is given by Gaussian elimination and the standard form of the parity check matrix in [15].…”

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Topological quantum codes from self-complementary self-dual graphs

Naghipour

Jafarizadeh

Shahmorad

2015

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In this paper we present two new classes of binary quantum codes with minimum distance of at least three, by self-complementary self-dual orientable embeddings of "voltage graphs" and "Paley graphs in the Galois field GF (p r )", where p ∈ P and r ∈ Z + . The parameters of two new classes of quantum codes are [[(2k ′ + 2)(8k ′ + 7), 2(8k ′2 + 7k ′ ), d min ]] and [[(2k ′ + 2)(8k ′ + 9), 2(8k ′2 + 9k ′ + 1), d min ]] respectively, where d min ≥ 3. For these quantum codes, the code rate approaches 1 as k ′ goes to infinity.

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