Results 1 to 10 of about 16,644 (310)
Some Bounds on the Size of Codes [PDF]
IEEE Transactions on Information Theory, 2014 We present some upper bounds on the size of non-linear codes and their restriction to systematic codes and linear codes. These bounds are independent of other known theoretical bounds, e.g. the Griesmer bound, the Johnson bound or the Plotkin bound, and one of these is actually an improvement of a bound by Litsyn and Laihonen. Our experiments show that
Emanuele Bellini, Massimiliano Sala
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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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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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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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Designs, Codes and Cryptography, 2021 The application of flags to network coding has been introduced recently by Liebhold, Nebe, and Vazquez-Castro. It is a variant to random linear network coding and explicit routing solutions for given networks. Here we study lower and upper bounds for the maximum possible cardinality of a corresponding flag code with given parameters.
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A Bound on Permutation Codes [PDF]
The Electronic Journal of Combinatorics, 2013 Consider the symmetric group $S_n$ with the Hamming metric. A permutation code on $n$ symbols is a subset $C\subseteq S_n.$ If $C$ has minimum distance $\geq n-1,$ then $\vert C\vert\leq n^2-n.$ Equality can be reached if and only if a projective plane of order $n$ exists.
Jürgen Bierbrauer, Klaus Metsch
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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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