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Hamming Matrix and Hamming Energy of a Graph

Match Communications in Mathematical and in Computer Chemistry
Hamming 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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On the rank of π1(Ham)

Algebraic & Geometric Topology, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Eigenvalues of Hamming Matrix and Hamming Energy of a Graph

Creative Mathematics and Informatics
Let 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

1991
Nach 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., 2004
Summary: 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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Ham: Cooked Ham

2016
F. Toldrá, M. Reig
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Hamming, Permutations and Automata

2007
Quantum 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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