Extending binary linear codes to self-orthogonal codes
, 2021 Kim et al. (2021) gave a method to embed a given binary $[n,k]$ code $\mathcal{C}$ $(k = 3, 4)$ into a self-orthogonal code of the shortest length which has the same dimension $k$ and minimum distance $d' \ge d(\mathcal{C})$. We extend this result by proposing a new method related to a special matrix, called the self-orthogonality matrix $SO_k ...
Kim, Jon-Lark, Choi, Whan-Hyuk
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A Construction of Quantum LDPC Codes from Cayley Graphs [PDF]
, 2013 We study a construction of Quantum LDPC codes proposed by MacKay, Mitchison and Shokrollahi. It is based on the Cayley graph of Fn together with a set of generators regarded as the columns of the parity-check matrix of a classical code. We give a general
Couvreur, Alain +2 more
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New Binary Quantum Codes Derived From One-Generator Quasi-Cyclic Codes
IEEE Access, 2019 In this paper, we consider a family of one-generator quasi-cyclic (QC) codes and their applications in quantum codes construction. We give a sufficient condition for one-generator QC codes to be self-orthogonal with respect to the symplectic inner ...
Jingjie Lv, Ruihu Li, Junli Wang
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Log-Domain Decoding of Quantum LDPC Codes Over Binary Finite Fields
IEEE Transactions on Quantum Engineering, 2021 A quantum stabilizer code over $\operatorname{GF}(q)$ corresponds to a classical additive code over $\operatorname{GF}(q^2)$ that is self-orthogonal with respect to a symplectic inner product.
Ching-Yi Lai, Kao-Yueh Kuo
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A three-dimensional, iterative mapping procedure for the implementation of an ionosphere-magnetosphere anisotropic Ohm's law boundary condition in global magnetohydrodynamic simulations [PDF]
Annales Geophysicae, 1995 The mathematical formulation of an iterative procedure for the numerical implementation of an ionosphere-magnetosphere (IM) anisotropic Ohm's law boundary condition is presented.
M. L. Goodman
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Duality of codes over non-unital rings of order six
AIMS MathematicsSome basic theory on the duality of codes over two non-unital rings of order $ 6 $, namely $ H_{23} $ and $ H_{32} $ is presented. For a code $ {{\mathcal C}} $ over these rings, there is an associated binary code $ {{\mathcal C}}_a $ and a ternary code $
Altaf Alshuhail +2 more
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Divergence coding for convolutional codes
MATEC Web of Conferences, 2017 In the paper we propose a new coding/decoding on the divergence principle. A new divergent multithreshold decoder (MTD) for convolutional self-orthogonal codes contains two threshold elements.
Valery Zolotarev +4 more
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A Genetically Encoded Isonitrile Lysine for Orthogonal Bioorthogonal Labeling Schemes
Molecules, 2021 Bioorthogonal click-reactions represent ideal means for labeling biomolecules selectively and specifically with suitable small synthetic dyes. Genetic code expansion (GCE) technology enables efficient site-selective installation of bioorthogonal handles ...
Ágnes Szatmári +8 more
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Simple Rate-1/3 Convolutional and Tail-Biting Quantum Error-Correcting Codes
, 2005 Simple rate-1/3 single-error-correcting unrestricted and CSS-type quantum convolutional codes are constructed from classical self-orthogonal $\F_4$-linear and $\F_2$-linear convolutional codes, respectively.
Forney, Jr., G. David, Guha, Saikat
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Quantum Error Correction via Codes over GF(4) [PDF]
, 1996 The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product.
Calderbank, A. R. +3 more
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