Universal Network Error Correction MDS Codes

The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem, together with the one-Mannheim error channel, where the error values are limited to the Mannheim weight one. Due to the limited error values, the codes over Gaussian integers achieve a higher error correction capability than maximum distance separable (MDS) codes with bounded minimum distance decoding. This higher error correction capability improves the work factor regarding decoding attacks based on information-set decoding. The codes also enable a low complexity decoding algorithm for decoding beyond the guaranteed error correction capability. In this work, we extend this coding scheme to codes over Eisenstein integers. These codes have advantages for the Niederreiter system. Additionally, we propose an improved code construction based on generalized concatenated codes. These codes extend to the rate region, where the work factor is beneficial compared to MDS codes. Moreover, generalized concatenated codes are more robust against structural attacks than ordinary concatenated codes.

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Matroidal error correction networks and linear network error correction MDS codes

Wuhan University Journal of Natural Sciences ◽

10.1007/s11859-013-0960-6 ◽

2013 ◽

Vol 18 (6) ◽

pp. 477-483

Author(s):

Hang Zhou ◽

Guangjun Liu

Keyword(s):

Error Correction ◽

Mds Codes ◽

Linear Network

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MDS Codes With Hulls of Arbitrary Dimensions and Their Quantum Error Correction

IEEE Transactions on Information Theory ◽

10.1109/tit.2018.2874953 ◽

2019 ◽

Vol 65 (5) ◽

pp. 2944-2952 ◽

Cited By ~ 20

Author(s):

Gaojun Luo ◽

Xiwang Cao ◽

Xiaojing Chen

Keyword(s):

Error Correction ◽

Quantum Error Correction ◽

Mds Codes ◽

Arbitrary Dimensions ◽

Quantum Error

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On quantum tensor product codes

Quantum Information and Computation ◽

10.26421/qic17.13-14-3 ◽

2017 ◽

Vol 17 (13&14) ◽

pp. 1105-1122

Author(s):

Jihao Fan ◽

Yonghui Li ◽

Min-Hsiu Hsieh ◽

Hanwu Chen

Keyword(s):

Tensor Product ◽

Error Correction ◽

Mds Codes ◽

Quantum Codes ◽

Multiple Quantum ◽

Parity Check ◽

Product Codes ◽

Burst Error ◽

Quantum Error ◽

Better Than

We present a general framework for the construction of quantum tensor product codes (QTPC). In a classical tensor product code (TPC), its parity check matrix is constructed via the tensor product of parity check matrices of the two component codes. We show that by adding some constraints on the component codes, several classes of dual-containing TPCs can be obtained. By selecting different types of component codes, the proposed method enables the construction of a large family of QTPCs and they can provide a wide variety of quantum error control abilities. In particular, if one of the component codes is selected as a burst-error-correction code, then QTPCs have quantum multiple-burst-error-correction abilities, provided these bursts fall in distinct subblocks. Compared with concatenated quantum codes (CQC), the component code selections of QTPCs are much more flexible than those of CQCs since only one of the component codes of QTPCs needs to satisfy the dual-containing restriction. We show that it is possible to construct QTPCs with parameters better than other classes of quantum error-correction codes (QECC), e.g., CQCs and quantum BCH codes. Many QTPCs are obtained with parameters better than previously known quantum codes available in the literature. Several classes of QTPCs that can correct multiple quantum bursts of errors are constructed based on reversible cyclic codes and maximum-distance-separable (MDS) codes.

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