Results 31 to 40 of about 3,225,248 (329)
Perfect codes in circulant graphs [PDF]
Discrete Mathematics, 2017 A perfect code in a graph =(V,E) is a subset C of V that is an independent set such that every vertex in VC is adjacent to exactly one vertex in C. A total perfect code in is a subset C of V such that every vertex of V is adjacent to exactly one vertex ...
Rongquan Feng, He Huang, Sanming Zhou
semanticscholar +1 more source
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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The Existence of Perfect Codes in Doob Graphs [PDF]
IEEE Transactions on Information Theory, 2018 We solve the problem of existence of perfect codes in the Doob graph. It is shown that 1-perfect codes in the Doob graph $ {D(m,n)}$ exist if and only if $6 {m}+3 {n}+1$ is a power of 2; that is, if the size of a 1-ball divides the number of vertices.
D. Krotov
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Additive perfect codes in Doob graphs [PDF]
Designs, Codes and Cryptography, 2018 The Doob graph D(m, n) is the Cartesian product of m>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength ...
Minjia Shi, Daitao Huang, D. Krotov
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New Results on Binary Codes Obtained by Doubling Construction
Cybernetics and Information Technologies, 2018 Binary codes created by doubling construction, including quasi-perfect ones with distance d = 4, are investigated. All [17·2r−6, 17·2r−6 − r, 4] quasi-perfect codes are classified.
Davydov Alexander A. +2 more
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Codes parameterized by the edges of a bipartite graph with a perfect matching
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this paper we study the main characteristics of some evaluation codes parameterized by the edges of a bipartite graph with a perfect matching.
Sarabia Manuel González +1 more
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Cyclotomic graphs and perfect codes [PDF]
Journal of Pure and Applied Algebra, 2015 We study two families of cyclotomic graphs and perfect codes in them. They are Cayley graphs on the additive group of Z [ ζ m ] / A , with connection sets { ± ( ζ m i + A ) : 0 ≤ i ≤ m − 1 } and { ± ( ζ m i + A ) : 0 ≤ i ≤ ϕ ( m ) − 1 } , respectively ...
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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Perfect codes in the lp metric [PDF]
European journal of combinatorics (Print), 2015 We investigate perfect codes in Z n in the ? p metric. Upper bounds for the packing radius r of a linear perfect code, in terms of the metric parameter p and the dimension n are derived.
A. Campello +3 more
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THE CLASS OF PERFECT TERNARY ARRAYS
Системный анализ и прикладная информатика, 2018 In recent decades, perfect algebraic constructions are successfully being use to signal systems synthesis, to construct block and stream cryptographic algorithms, to create pseudo-random sequence generators as well as in many other fields of science and ...
A. V. Sokolov, O. N. Zhdanov
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