Hamiltonicity of Minimum Distance Graphs of 1-Perfect Codes
نویسندگان
چکیده
منابع مشابه
Hamiltonicity of Minimum Distance Graphs of 1-Perfect Codes
A 1-perfect code Cn q is called Hamiltonian if its minimum distance graph G(Cn q ) contains a Hamiltonian cycle. In this paper, for all admissible lengths n ≥ 13, we construct Hamiltonian nonlinear ternary 1-perfect codes, and for all admissible lengths n ≥ 21, we construct Hamiltonian nonlinear quaternary 1-perfect codes. The existence of Hamiltonian nonlinear q-ary 1-perfect codes of length N...
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An extended 1-perfect code C folds over its kernel via the Steiner quadruple systems associated with its codewords. The resulting folding, proposed as a graph invariant for C, distinguishes among the 361 nonlinear codes C of kernel dimension κ with 9 ≥ κ ≥ 5 obtained via Solov’eva-Phelps doubling construction. Each of the 361 resulting graphs has most of its nonloop edges expressible in terms o...
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The search for codes of covering radius 1 led Österg̊ard, Quistorff and Wassermann to the OQW method of associating a unique graph to each code [9]. We present results on the structure and existence of OQW-associated graphs. These are used to find an upper bound on the size of a ball of radius 1 around a code of length 3 and minimum distance 2. OQW-associated graphs and non-extendable partial La...
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We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in G. Let G be a graph of order n and λ (G) be the spectral radius of its adjacency matrix. One of the main results of the paper is the following theorem: Let k 2, n k3 + k + 4, and let G be a graph of order n, with minimum degree δ (G) k. If λ (G) n k 1, then G has a Hamiltonian cycle, unless G = K1 _ (Kn k...
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We study 1-perfect codes in Doob graphsD(m,n). We show that such codes that are linear over GR(4) exist if and only if n = (4γ+δ−1)/3 andm = (4γ+2δ−4γ+δ)/6 for some integers γ ≥ 0 and δ > 0. We also prove necessary conditions on (m,n) for 1-perfect codes that are linear over Z4 (we call such codes additive) to exist in D(m,n) graphs; for some of these parameters, we show the existence of codes....
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2012
ISSN: 1077-8926
DOI: 10.37236/2158