Determining the Upper-Bound on the Code Distance of Quantum Stabilizer Codes Through the Monte Carlo Method Based on Fully Decoupled Belief Propagation [PDF]
EntropyThe code distance is a critical parameter of quantum stabilizer codes (QSCs), and determining it—whether exactly or approximately—is known to be an NP-complete problem.
Zhipeng Liang +4 more
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Combinatorial Alphabet-Dependent Bounds for Locally Recoverable Codes
IEEE Transactions on Information Theory, 2018 Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems.
Abhishek Agarwal +2 more
exaly +3 more sources
Refinements and Generalizations of the Shannon Lower Bound via Extensions of the Kraft Inequality [PDF]
EntropyWe derive a few extended versions of the Kraft inequality for lossy compression, which pave the way to the derivation of several refinements and extensions of the well-known Shannon lower bound in a variety of instances of rate-distortion coding.
Neri Merhav
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New perspectives on covariant quantum error correction [PDF]
Quantum, 2021 Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an important case ...
Sisi Zhou, Zi-Wen Liu, Liang Jiang
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Connectivity constrains quantum codes [PDF]
Quantum, 2022 Quantum low-density parity-check (LDPC) codes are an important class of quantum error correcting codes. In such codes, each qubit only affects a constant number of syndrome bits, and each syndrome bit only relies on some constant number of qubits ...
Nouédyn Baspin, Anirudh Krishna
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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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Lower Bound on the Minimum Distance of Single-Generator Quasi-Twisted Codes
Mathematics, 2023 We recall a classic lower bound on the minimum Hamming distance of constacyclic codes over finite fields, analogous to the well-known BCH bound for cyclic codes.
Adel Alahmadi +2 more
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Gottesman-Kitaev-Preskill codes: A lattice perspective [PDF]
Quantum, 2022 We examine general Gottesman-Kitaev-Preskill (GKP) codes for continuous-variable quantum error correction, including concatenated GKP codes, through the lens of lattice theory, in order to better understand the structure of this class of stabilizer codes.
Jonathan Conrad +2 more
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Bounds on the Probability of Undetected Error for q-Ary Codes
Entropy, 2023 We study the probability of an undetected error for general q-ary codes. We give upper and lower bounds on this quantity, by the Linear Programming and the Polynomial methods, as a function of the length, size, and minimum distance.
Xuan Wang, Huizhou Liu, Patrick Solé
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A Decoding Algorithm for Convolutional Codes
Mathematics, 2022 It is shown how the decoding algorithms of Pellikaan and Rosenthal can be coupled to produce a decoding algorithm for convolutional codes. Bounds for the computational cost per decoded codeword are also computed.
Sandra Martín Sánchez +1 more
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