Results 11 to 20 of about 18,205,701 (285)
Perturbative Stability and Error-Correction Thresholds of Quantum Codes [PDF]
PRX QuantumTopologically ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding ...
Yaodong Li +2 more
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Linear codes resulting from finite group actions [PDF]
Transactions on Combinatorics, 2022 In this article, we use group action theory to define some important ternary linear codes. Some of these codes are self-orthogonal having a minimum distance achieving the lower bound in the previous records. Then, we define two new codes sharing the same
Driss Harzalla
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New Constructions of Optimal Linear Codes From Simplicial Complexes [PDF]
IEEE Transactions on Information Theory, 2023 In this paper, we construct a large family of projective linear codes over ${\mathbb F}_{q}$ from the general simplicial complexes of ${\mathbb F}_{q}^{m}$ via the defining-set construction, which generalizes the results of [IEEE Trans. Inf.
Zhao Hu +5 more
semanticscholar +1 more source
The Extended Codes of Some Linear Codes [PDF]
Finite Fields Their Appl., 2023 The classical way of extending an $[n, k, d]$ linear code $\C$ is to add an overall parity-check coordinate to each codeword of the linear code $\C$. This extended code, denoted by $\overline{\C}(-\bone)$ and called the standardly extended code of $\C ...
Zhong-Hua Sun, C. Ding, Ting Chen
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Minimal Binary Linear Codes From Vectorial Boolean Functions [PDF]
IEEE Transactions on Information Theory, 2022 Recently, much progress has been made to construct minimal linear codes due to their preference in secret sharing schemes and secure two-party computation.
Yan-Jun Li +3 more
semanticscholar +1 more source
Adaptive nested trellis decoding for block codes. [PDF]
, 1994 A new adaptive trellis decoding technique for block codes is proposed. The technique is based on an encoding technique which allows the design of almost all known linear codes together with their minimal trellises.
Markarian, G. S. +5 more
core +5 more sources
On Linear Codes With One-Dimensional Euclidean Hull and Their Applications to EAQECCs [PDF]
IEEE Transactions on Information Theory, 2021 The Euclidean hull of a linear code $C$ is the intersection of $C$ with its Euclidean dual $C^\perp $ . The hull with low dimensions gets much interest due to its crucial role in determining the complexity of algorithms for computing the ...
Sok Lin
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Quaternary Linear Codes and Related Binary Subfield Codes [PDF]
IEEE Transactions on Information Theory, 2021 In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and defining sets ...
Yan-Sheng Wu, Chengju Li, Fu Xiao
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Some Punctured Codes of Several Families of Binary Linear Codes [PDF]
IEEE Transactions on Information Theory, 2021 Two general constructions of linear codes with functions over finite fields have been extensively studied in the literature. The first one is given by $\mathcal {C}(f)=\{ {\mathrm{ Tr}}({\textit{af}}({x})+{\textit{bx}})_{x \in \mathbb {F}_{q^{m}}^{*}}: {
Xiao-Qiang Wang, Da-Bin Zheng, C. Ding
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Punctured Low-Bias Codes Behave Like Random Linear Codes [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2021 Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models.
V. Guruswami, Jonathan Mosheiff
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