Two new families of entanglement-assisted quantum MDS codes from generalized Reed–Solomon codes

Luo, Gaojun; Cao, Xiwang

doi:10.1007/s11128-019-2207-8

Cited by 46 publications

(18 citation statements)

References 20 publications

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“…By Theorem 4.3, taking some special q, we obtain new EAQEC MDS codes in Table 1. Compared to the EAQEC MDS codes in [26], we have that the distance of our EAQEC MDS codes obtained in Table 1 are larger than all of them.…”

Section: The First Classes Of Eaqec Mds Codesmentioning

confidence: 76%

A new method for constructing EAQEC MDS codes

Peng¹,

Liu²

2020

Preprint

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Entanglement-assisted quantum error-correcting (EAQEC) codes make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQEC code from any classical linear code, unlike standard quantum error-correcting codes, which can only be constructed from dual-containing codes. However, the number c of pre-shared maximally entangled states is usually calculated by computer search. In this paper, we first give a new formula for calculating the number c of pre-shared maximally entangled states. Then, using this formula, we construct three classes of new entanglement-assisted quantum error-correcting maximum-distance-separable ( EAQEC MDS) codes.

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Section: The First Classes Of Eaqec Mds Codesmentioning

confidence: 76%

A new method for constructing EAQEC MDS codes

Peng¹,

Liu²

2020

Preprint

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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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“…Several articles have explored the construction of EAQECCs from classical linear codes as binary BCH codes [8,18,21], constacyclic codes [17,27], constacyclic LCD codes [24], cyclic codes [25], generalized Reed-Solomon codes [14,19,20], negacyclic BCH codes [6,7] and algebraic-geometry codes [23]. These papers address particular cases and determine their parameters but no general formula for the parameters of EAQECCs using the previous families of codes is known.…”

Section: Introductionmentioning

confidence: 99%

Entanglement-assisted quantum error-correcting codes from RS codes and BCH codes with extension degree 2

Galindo

Hernando

Ruano

2021

Quantum Inf Process

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Entanglement-assisted quantum error-correcting codes (EAQECCs) constructed from Reed-Solomon codes and BCH codes are considered in this work. It is provided a complete and explicit formula for the parameters of EAQECCs coming from any Reed-Solomon code, for the Hermitian metric, and from any BCH code with extension degree 2 and consecutive cyclotomic cosets, for both the Euclidean and the Hermitian metric. The main task in this work is the computation of a completely general formula for c, the minimum number of required maximally entangled quantum states.

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Two new families of entanglement-assisted quantum MDS codes from generalized Reed–Solomon codes

Cited by 46 publications

References 20 publications

A new method for constructing EAQEC MDS codes

A new method for constructing EAQEC MDS codes

Development of a Reed-Solomon Error Detection and Correction System

Entanglement-assisted quantum error-correcting codes from RS codes and BCH codes with extension degree 2

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