Some new quantum MDS codes from generalized Reed–Solomon codes

Tian, Fuyin; Zhu, Shixin

doi:10.1016/j.disc.2019.07.009

Cited by 16 publications

(7 citation statements)

References 27 publications

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“…Corollary 3. ( [27]) Let q be an odd integer and n = ( h 2 + 2) q 2 −1 2h , where q−1 h = 2τ + 1 for some τ ≥ 1. Then for any 1 ≤ k ≤ (h+2) q−1 2h , there exists a quantum MDS code with parameters [[n, n−2k, k +1]] q .…”

Section: Hmentioning

confidence: 99%

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MDS constacyclic codes of length q + 1 over GF(q)

et al. 2023

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An important family of quantum codes is the quantum maximum-distance-separable (MDS) codes. In this paper, we construct some new classes of quantum MDS codes by generalized Reed-Solomon (GRS) codes and Hermitian construction. In addition, the length n of most of the quantum MDS codes we constructed satisfies n ≡ 0, 1(mod q±12 ), which is different from previously known code lengths. At the same time, the quantum MDS codes we construct have large minimum distances that are greater than q/2 + 1.

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Section: Hmentioning

confidence: 99%

“…Corollary 1. ( [27]) Let q be an odd integer and n = ( h 2 + 1) q 2 −1 2h , where q−1 h = 2τ + 1 for some τ ≥ 1.…”

mentioning

confidence: 99%

MDS constacyclic codes of length q + 1 over GF(q)

et al. 2023

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“…in [22,23,24,25,25,26,27,28,29,30,31,32,33,34,35,45]. For other researches on the construction of Hermitian self-orthogonal codes from cyclic codes, constacyclic codes, negacyclic codes, graph theory and so on, we refer to [36,37,38,39,40].…”

Section: Et Al Constructed Mds Codes With Arbitrary-dimensional E-gal...mentioning

confidence: 99%

On Arbitrary Dimension Hermitian Hull linear codes from Hermitian self-orthogonal codes and New Hermitian Self-Orthogonal GRS Codes

Li¹,

Zhu²

2022

Preprint

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Due to the important role of hulls of linear codes in coding theory, the problem about constructing arbitrary dimension hull linear codes has become a hot issue. In this paper, we generalize conclusions in [41] and [42] and prove that the self-orthogonal codes of length n can construct linear codes of length n + 2i and n + 2i + 1 with arbitrary-dimensional hulls under the special Hermitian inner product and the general e-Galois inner product for any integers i ≥ 0. Then four new classes of Hermitian self-orthogonal GRS or extend GRS codes are constructed via two known multiplicative coset decompositions of F q 2 . The codes we constructed can be used to obtain new arbitrary dimension Galois hull linear codes by Theorems 11 and 12 in [21] and finally we get many new EAQECCs whose code lengths can take n + 2i and n + 2i + 1.

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“…Traditionally, quantum codes were only studied in the symmetric case, but by now the literature contains a great number of works studying either of the two types of codes. In this work, we only consider symmetric codes, and some recent developments in this field are [7,18,19,21,22,25,31]. In this setting, the code parameters are commonly written in the form [[n, k, d]] q , and we will follow this convention.…”

Section: Introductionmentioning

confidence: 99%

On Steane-enlargement of quantum codes from Cartesian product point sets

Christensen

Geil

2020

Quantum Inf Process

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In this work, we study quantum error-correcting codes obtained by using Steaneenlargement. We apply this technique to certain codes defined from Cartesian products previously considered by Galindo et al. in [8]. We give bounds on the dimension increase obtained via enlargement, and additionally give an algorithm to compute the true increase. A number of examples of codes are provided, and their parameters are compared to relevant codes in the literature, which shows that the parameters of the enlarged codes are advantageous. Furthermore, comparison with the Gilbert-Varshamov bound for stabilizer quantum codes shows that several of the enlarged codes match or exceed the parameters promised by the bound.

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Some new quantum MDS codes from generalized Reed–Solomon codes

Cited by 16 publications

References 27 publications

MDS constacyclic codes of length q + 1 over GF(q)

MDS constacyclic codes of length q + 1 over GF(q)

On Arbitrary Dimension Hermitian Hull linear codes from Hermitian self-orthogonal codes and New Hermitian Self-Orthogonal GRS Codes

On Steane-enlargement of quantum codes from Cartesian product point sets

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