Results 11 to 20 of about 113,006 (300)
Advances in Mathematics of Communications, 2008 The first examples of perfect $e$-error correcting $q$-ary codes were given in the 1940's by Hamming and Golay. In 1973 Tietavainen, and independently Zinoviev and Leontiev, proved that if q is a power of a prime number then there are no unknown multiple error correcting perfect $q$-ary codes. The case of single error correcting perfect codes is quite
Heden, Olof
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Perfect codes in power graphs of finite groups
Open Mathematics, 2017 The power graph of a finite group is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. The enhanced power graph of a finite group is the graph whose vertex set consists of all elements of the ...
Ma Xuanlong +4 more
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Discrete Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Heden, Olof, Olof Heden, Heden, Olof,
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On the reconstruction of perfect codes
Discrete Mathematics, 2002 For a perfect 1-error correcting binary code \(C\), let \(C(k)\) denote the set of words of \(C\) of weight \(k\). \textit{S. V. Avgustinovich} [Discrete Anal. Issled. Oper. 2, 4-6 (1995; Zbl 0846.94017, Zbl 0861.94018)] has shown that if \(C((n+ 1)/2)= C'((n+ 1)/2)\) for two binary perfect 1-error correcting codes \(C\) and \(C'\) of length \(n\) then
Heden, Olof
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Journal of Combinatorial Designs, 2023 AbstractA multifold 1‐perfect code (1‐perfect code for list decoding) in any graph is a set of vertices such that every vertex of the graph is at distance not more than 1 from exactly elements of . In ‐ary Hamming graphs, where is a prime power, we characterize all parameters of multifold 1‐perfect codes and all parameters of additive multifold 1 ...
Krotov, Denis S.
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The XYZ$^2$ hexagonal stabilizer code [PDF]
Quantum, 2022 We consider a topological stabilizer code on a honeycomb grid, the "XYZ$^2$" code. The code is inspired by the Kitaev honeycomb model and is a simple realization of a "matching code" discussed by Wootton [J. Phys. A: Math. Theor. 48, 215302 (2015)], with
Basudha Srivastava +2 more
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Perfect codes in the discrete simplex [PDF]
Designs, Codes and Cryptography, 2013 We study the problem of existence of (nontrivial) perfect codes in the discrete $ n $-simplex $ Δ_{\ell}^n := \left\{ \begin{pmatrix} x_0, \ldots, x_n \end{pmatrix} : x_i \in \mathbb{Z}_{+}, \sum_i x_i = \ell \right\} $ under $ \ell_1 $ metric. The problem is motivated by the so-called multiset codes, which have recently been introduced by the authors ...
Mladen Kovacevic 0001 +1 more
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IEEE Transactions on Information Theory, 2011 In this paper we consider completely regular codes, obtained from perfect (Hamming) codes by lifting the ground field. More exactly, for a given perfect code C of length n=(q^m-1)/(q-1) over F_q with a parity check matrix H_m, we define a new code C_{(m,r)} of length n over F_{q^r}, r > 1, with this parity check matrix H_m.
Josep Rifà, Victor A. Zinoviev
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Perfect Codes in Cayley Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2018 This is the final version that will appear in SIAM J.
He Huang, Binzhou Xia, Sanming Zhou
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Multi-path Summation for Decoding 2D Topological Codes [PDF]
Quantum, 2018 Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance.
Ben Criger, Imran Ashraf
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