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

Galindo, Carlos; Hernando, Fernando

doi:10.1007/s10623-022-01018-2

Cited by 7 publications

(3 citation statements)

References 42 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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“…This implies that it truncates to codes equivalent to Hermitian self-orthogonal codes of length 9, 12 and 15 and one can check that these codes are a [9,4] It was proven in [3] that a [9,4,6] 9 MDS code does not come from a truncation of a generalised Reed-Solomon code. The only [9,4,6] 9 code which is not the truncation of a generalised Reed-Solomon code is the projection of Glynn's [10,5,6] 9 MDS code, see [6].…”

Section: Hermitian Self-orthogonal Codesmentioning

confidence: 99%

The geometry of Hermitian self-orthogonal codes

Ball¹,

Vilar²

2021

Preprint

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We prove that if n > k 2 then a k-dimensional linear code of length n over F q 2 has a truncation which is linearly equivalent to a Hermitian self-orthogonal linear code. In the contrary case we prove that truncations of linear codes to codes equivalent to Hermitian self-orthogonal linear codes occur when the columns of a generator matrix of the code do not impose independent conditions on the space of Hermitian forms. In the case that there are more than n common zeros to the set of Hermitian forms which are zero on the columns of a generator matrix of the code, the additional zeros give the extension of the code to a code that has a truncation which is equivalent to a Hermitian self-orthogonal code.

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“…Many of these codes satisfy K = q k , for some nonnegative integer k, and then their parameters are expressed as [[n, k, d]] q ; abusing the notation we say that k is the dimension of these codes. QECCs were first introduced in the binary case [10,22,9,4,5] and later in the general case [7,3,30,1,32,11,17,18], where we have cited only some references of a vast literature on the subject. QECCs in the nonbinary case are convenient for fault-tolerant quantum computation [43,31,23,36].…”

Section: Introductionmentioning

confidence: 99%

Steane enlargement of Entanglement-Assisted Quantum Error-Correcting Codes

Galindo¹,

Hernando²,

Matsumoto³

2023

Preprint

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

Abstract: 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 … Show more

Cited by 7 publications

References 42 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

The geometry of Hermitian self-orthogonal codes

Steane enlargement of Entanglement-Assisted Quantum Error-Correcting Codes

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