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Some new QEC MDS codes with large minimum distance [PDF]
Scientific ReportsThe advancement of Quantum Error-Correcting (QEC) Maximum Distance Separable (MDS) codes holds substantial importance in practical applications, substantially augmenting the reliability and efficiency of quantum communication and computing.
Lanqiang Li +3 more
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Quantum Codes from Galois Hulls of Constacyclic Codes over a Finite Non-Chain Ring [PDF]
EntropyWe study the algebraic structures of constacyclic codes over a new finite non-chain ring R and their l-Galois dual codes based on a new Gray map ϕ and determine the dimensions of the l-Galois hull of constacyclic codes over R.
Enbin Zhang, Bo Kong, Xiying Zheng
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Quantum Codes of Maximal Distance and Highly Entangled Subspaces [PDF]
Quantum, 2020 We present new bounds on the existence of general quantum maximum distance separable codes (QMDS): the length $n$ of all QMDS codes with local dimension $D$ and distance $d \geq 3$ is bounded by $n \leq D^2 + d - 2$.
Felix Huber, Markus Grassl
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A New Class of Q-Ary Codes for the McEliece Cryptosystem
Cryptography, 2021 The McEliece cryptosystem is a promising candidate for post-quantum public-key encryption. In this work, we propose q-ary codes over Gaussian integers for the McEliece system and a new channel model.
Jürgen Freudenberger +1 more
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Projective MDS Codes Over GF(27)
مجلة بغداد للعلوم, 2021 MDS code is a linear code that achieves equality in the Singleton bound, and projective MDS (PG-MDS) is MDS code with independents property of any two columns of its generator matrix.
Emad Bakr Abdulkareem Al-Zangana
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Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography
Cryptography, 2021 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 ...
Johann-Philipp Thiers +1 more
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New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields
Entropy, 2019 Maximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality.
Aixian Zhang, Zhe Ji
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IEEE Access, 2020 Let p ≠ 3 be any prime. The structures of all λ-constacyclic codes of length 3ps over the finite commutative chain ring Fpm + uFpm (u2 = 0) are established in the term of their generator polynomials.
Hai Q. Dinh +2 more
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Breaking the MDS-PIR Capacity Barrier via Joint Storage Coding
Information, 2019 The capacity of private information retrieval (PIR) from databases coded using maximum distance separable (MDS) codes was previously characterized by Banawan and Ulukus, where it was assumed that the messages are encoded and stored separably in the ...
Hua Sun, Chao Tian
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Some Connections Between Classical Coding and Network Coding Over Erroneous Cyclic Networks
IEEE Access, 2016 Recently, a framework was given for linear error-correcting network codes (LENCs) over cyclic networks on commutative rings. When the alphabet is considered as a rational power series ring, an LENC is referred to as a convolutional error-correcting ...
Vahid Samadi-Khaftari +2 more
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