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Hamming Matrix and Hamming Energy of a Graph
Match Communications in Mathematical and in Computer ChemistryHamming distance is a highly valuable quantity in computer science. In this work, we establish the Hamming matrix H of a graph G, H(G). This is a square matrix, where the elements of the H(G) are Hamming distances. Also, we define the Hamming energy of a graph, HE(G), which is a sum of the absolute eigenvalues of H(G).
Nemanja Vučićević +2 more
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Algebraic & Geometric Topology, 2022
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On the Eigenvalues of Hamming Matrix and Hamming Energy of a Graph
Creative Mathematics and InformaticsLet G be a graph with n vertices and m edges. Let V(G) = {v1,v2,...,vn} be the vertex set of G. Thestring s(vi) is the row in the incidence matrix of G corresponding to the vertex vi, which is an m-tuple in Zm 2 . The Hamming matrix H(G) = [hij] of a graph G is an n×nmatrix, whose (i,j)-th entry is the Hamming distance between the strings s(vi) and
HARISHCHANDRA S. RAMANE +2 more
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Hamming-Codes und erweiterte Hamming-Codes
1991Nach Satz 11.5c kann man einen 1-fehlerkorrigierenden binaren Code konstruieren, indem man als Kontrollmatrix eine Matrix mit paarweise verschiedenen Spalten ungleich 0 nimmt. Wir behandeln nun den Fall mit maximaler Spaltenzahl n bei gegebener Zeilenzahl r (- dabei ist r = n – k die Anzahl der Paritatskontrollen). Es existieren genau n = 2 r – 1 von 0
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On computing the Hamming distance
Acta Cybern., 2004Summary: Methods for the fast computation of the Hamming distance developed for the case of a large number of pairs of words are presented and discussed in the paper. The connection of this subject to some questions about intersecting sets and Hadamard designs is also considered.
Gerzson Kéri, Ákos Kisvölcsey
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Hamming, Permutations and Automata
2007Quantum finite automata with mixed states are proved to be super-exponentially more concise rather than quantum finite automata with pure states. It was proved earlier by A.Ambainis and R.Freivalds that quantum finite automata with pure states can have exponentially smaller number of states than deterministic finite automata recognizing the same ...
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