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Multifold 1‐perfect codes [PDF]
Journal of Combinatorial Designs, 2022 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 ...
D. Krotov
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Lattice-Like Total Perfect Codes
Discussiones Mathematicae Graph Theory, 2014 A contribution is made to the classification of lattice-like total perfect codes in integer lattices Λn via pairs (G, Φ) formed by abelian groups G and homomorphisms Φ: Zn → G.
Araujo Carlos, Dejter Italo
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Perfect codes in Doob graphs [PDF]
Designs, Codes, and Cryptography, 2015 11pp
Denis S Krotov, Krotov Denis S
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Characterizing subgroup perfect codes by 2-subgroups [PDF]
Designs, Codes and Cryptography, 2022 A perfect code in a graph $$\Gamma $$ Γ is a subset C of $$V(\Gamma )$$ V ( Γ ) such that no two vertices in C are adjacent and every vertex in $$V(\Gamma ){\setminus } C$$ V ( Γ ) \ C is adjacent to exactly one vertex in C .
Junyang Zhang
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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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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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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
Olof Héden
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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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Transitive nonpropelinear perfect codes [PDF]
Discrete Mathematics, 2015 Accepted to Discrete ...
Ivan Yu. Mogilnykh, Faina I. Solov'eva
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Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors [PDF]
International Symposium on Information Theory, 2022 Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These codes are lattices that tile the integer grid with the appropriate error ball.
Hengjia Wei, Moshe Schwartz
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