Entanglement-assisted quantum MDS codes from generalized Reed–Solomon codes

Li, Lanqiang; Zhu, Shixin; Liu, Li; Kai, Xiaoshan

doi:10.1007/s11128-019-2269-7

Cited by 27 publications

(7 citation statements)

References 29 publications

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“…This may help them for future studies and which also may lead to new knowledge and discoveries, thus, helping them through the course of electronics. The design of the system is mainly composed of input, encoder, and decoder, from what the group has understood [8,9]. The first block of the design was the input, whether it be an integer or a certain kind of message.…”

Section: Significance Of the Studymentioning

confidence: 99%

Development of a Reed-Solomon Error Detection and Correction System

Africa¹

2020

IJETER

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This project scopes into the Reed-Solomon (RS) Code as one of the optimal error detection and correction schemes. RS codes are codes in which adding unnecessary bits to a data in order for it to be reliably recovered even though the presence of errors in transferal, cache, and retrieval, is executed. The encoder for this specific code differs from a binary encoder in that it operates on the multiple bits rather than individual bits giving it the ability to precisely detect and correct error compared to other error and correction schemes. Its unique algorithm may be used in any analog or digital communication system because of it having the highest efficient use of redundancy, ability to adjust block length has a wide range of code rate and is an efficient coding technique perfect for accurate and precise code error detection. Storage devices, wireless communication, satellite communication, digital television, and high-speed modems are constructs of Reed-Solomon.

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Section: Significance Of the Studymentioning

confidence: 99%

Development of a Reed-Solomon Error Detection and Correction System

Africa¹

2020

IJETER

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“…Based on these effects, researches on the Hull of linear codes have become a hot issue in resent years. Generally speaking, when people construct EAQECCs, they usually firstly construct linear codes (often MDS codes) with arbitrary-dimensional hulls including the Euclidean, Hermitian and Galois cases, such as [15,16,17,18,19,20,21,46]. In particular, in [20] and [21], Fang et al and…”

Section: Introductionmentioning

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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“…Specifically, we refer to [16] for the usual Euclidean and classical Hermitian cases, and [29] for the general Galois case. Based on these outstanding results, a large number of MDS codes (i.e., d = n − k + 1) with Euclidean hulls and Hermitian hulls of arbitrary dimensions were constructed and so many EAQECCs were given in [7,12,17,23,24,26,30,39] and references therein.…”

Section: Introductionmentioning

confidence: 99%

On MDS Codes With Galois Hulls of Arbitrary Dimensions

Zhu

2022

Preprint

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The Galois hulls of linear codes are a generalization of the Euclidean and Hermitian hulls of linear codes. In this paper, we study the Galois hulls of (extended) GRS codes and present several new constructions of MDS codes with Galois hulls of arbitrary dimensions via (extended) GRS codes. Two general methods of constructing MDS codes with Galois hulls of arbitrary dimensions by Hermitian or general Galois self-orthogonal (extended) GRS codes are given. Using these methods, some MDS codes with larger dimensions and Galois hulls of arbitrary dimensions can be obtained and relatively strict conditions can also lead to many new classes of MDS codes with Galois hulls of arbitrary dimensions. 2010 MSC: 12E20, 81p70

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Entanglement-assisted quantum MDS codes from generalized Reed–Solomon codes

Cited by 27 publications

References 29 publications

Development of a Reed-Solomon Error Detection and Correction System

Development of a Reed-Solomon Error Detection and Correction System

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

On MDS Codes With Galois Hulls of Arbitrary Dimensions

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