Search results for "Hamming code"
showing 5 items of 5 documents
Automatic mass spectra recognition for Ultra High Vacuum systems using multilabel classification
2021
Abstract In Ultra High-Vacuum (UHV) systems it is common to find a mixture of many gases originating from surface outgassing, leaks and permeation that contaminate vacuum chambers and cause issues to reach ultimate pressures. The identification of these contaminants is, in general, done manually by trained technicians from the analysis of mass spectra. This task is time consuming and can lead to misinterpretation or partial understanding of issues. The challenge resides in the rapid identification of these contaminants by using some automatic gas identification technique. This paper explores the automatic and simultaneous identification of 80 molecules, including some of the most commonly p…
On strongly tactical codes
1986
We study perfect error correcting codes in which the codewords are protected by Hamming spheres of distinct protective radii. These codes have been introduced by Cohen, Montaron and Frankl [3, 4, 10].
NP-completeness of the hamming salesman problem
1985
It is shown that the traveling salesman problem, where cities are bit strings with Hamming distances, is NP-complete.
Binary Hamming codes and Boolean designs
2021
AbstractIn this paper we consider a finite-dimensional vector space $${\mathcal {P}}$$ P over the Galois field $${\text {GF}}(2),$$ GF ( 2 ) , and the family $${\mathcal {B}}_k$$ B k (respectively, $${\mathcal {B}}_k^*$$ B k ∗ ) of all the k-sets of elements of $$\mathcal {P}$$ P (respectively, of $${\mathcal {P}}^*= {\mathcal {P}} \setminus \{0\}$$ P ∗ = P \ { 0 } ) summing up to zero. We compute the parameters of the 3-design $$({\mathcal {P}},{\mathcal {B}}_k)$$ ( P , B k ) for any (necessarily even) k, and of the 2-design $$({\mathcal {P}}^{*},{\mathcal {B}}_k^{*})$$ ( P ∗ , B k ∗ ) for any k. Also, we find a new proof for the weight distribution of the binary Hamming code. Moreover, we…
On the weight distribution of perfect binary codes
2021
In this paper, we give a new proof of the closed-form formula for the weight distribution of a perfect binary single-error-correcting code.