New quantum MDS codes over finite fields

Fang, Xiaolei; Luo, Jinquan

doi:10.1007/s11128-019-2506-0

Cited by 21 publications

(14 citation statements)

References 28 publications

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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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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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“…Lemma 4.1 serves as a foundation for numerous constructions of quantum MDS codes based on their connection to Hermitian self-orthogonal MDS codes, as exemplified in [9,12,11,17,20,23,24,25,26,27,31,30,37,38,39,41,42,13,18,19].…”

Section: 1mentioning

confidence: 99%

“…The constructions of quantum codes, in particular, have been investigated extensively in the past two decades. The works in [9,12,11,17,20,23,24,25,26,27,31,30,37,38,39,41,42,13,18,19,40,21] and the references therein form a partial list of an already vast and still rapidly growing literature.…”

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confidence: 99%

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Two new classes of Hermitian self-orthogonal non-GRS MDS codes and their applications

Luo

Cao

Ezerman

et al. 2022

AMC

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<p style='text-indent:20px;'>Hermitian self-orthogonal codes form an essential ingredient in the construction of quantum stabilizer codes. In this paper, we present two new classes of Hermitian self-orthogonal MDS codes from twisted generalized Reed-Solomon codes. The constructed codes are monomially inequivalent to generalized Reed-Solomon codes. Two new classes of Hermitian LCD MDS codes can then be derived. Finally, based on the constructed Hermitian self-orthogonal MDS codes, we present two classes of quantum MDS codes with new parameters.</p>

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“…As in the classical case, quantum MDS codes are one of the extremely useful and interesting quantum codes in quantum error correction. The construction of quantum MDS codes has become one of the major themes in recent years (see [2,7,6,8,13,14,15,16,18,19,3,17,5]).…”

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confidence: 99%

Some new quantum MDS codes derived from generalized Reed-Solomon codes

Shi

Yue

2022

AMC

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<p style='text-indent:20px;'>Quantum maximum-distance-separable (MDS) codes are very important in coding theory. In this paper, we construct three classes of new quantum MDS codes with large minimum distance by classical Hermitian self-orthogonal generalized Reed-Solomon codes. Furthermore, these quantum MDS codes have more flexible lengths and larger minimum distance than those of some known quantum MDS codes.</p>

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New quantum MDS codes over finite fields

Cited by 21 publications

References 28 publications

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

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

Two new classes of Hermitian self-orthogonal non-GRS MDS codes and their applications

Some new quantum MDS codes derived from generalized Reed-Solomon codes

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