Results 1 to 10 of about 18,689 (154)
On some batch code properties of the simplex code
Designs, Codes, and Cryptography, 2022 The binary $k$-dimensional simplex code is known to be a $2^{k-1}$-batch code and is conjectured to be a $2^{k-1}$-functional batch code. Here, we offer a simple, constructive proof of a result that is "in between" these two properties. Our approach is to relate these properties to certain (old and new) additive problems in finite abelian groups.
Henk D L Hollmann +2 more
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On Best Erasure Wiretap Codes: Equivocation Matrices and Design Principles [PDF]
EntropyPhysical-layer security can aid in establishing secure telecommunication networks including cellular, Internet of Things, and telemetry networks, among others. Channel sounding techniques and/or telemetry systems for reporting channel conditions, coupled
Willie K. Harrison +3 more
doaj +2 more sources
The Complete Hierarchical Locality of the Punctured Simplex Code [PDF]
2019 IEEE International Symposium on Information Theory (ISIT), 2019 AbstractThis paper presents a new alphabet-dependent bound for codes with hierarchical locality. Then, the complete list of possible localities is derived for a class of codes obtained by deleting specific columns from a Simplex code. This list is used to show that these codes are optimal codes with hierarchical locality.
Matthias Grezet, Camilla Hollanti
exaly +8 more sources
On the cosets of the simplex code
Discrete Mathematics, 1985 Weight and distance properties of cosets of the simplex code are investigated. Let \(S_ m\) be the \((2^ m-1\), m, \(2^{m-1})\) simplex code and S its extension. It is shown that the coset of the all-1 vector of the extended code S of type \((2^ m\), m, \(2^{m-1})\) is the only coset of maximum weight \((2^{m-1})\).
Tor Helleseth, H F Mattson
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On maximal cliques in the graph of simplex codes
Journal of GeometryThe induced subgraph of the corresponding Grassmann graph formed by simplex codes is considered. We show that this graph, as the Grassmann graph, contains two types of maximal cliques. For any two cliques of the first type there is a monomial linear automorphism transferring one of them to the other.
Mariusz Kwiatkowski +2 more
exaly +4 more sources
The Pyrenean species of Chelidura (Dermaptera, Forficulidae) [PDF]
Deutsche Entomologische Zeitschrift, 2021 The Pyrenees are inhabited by scattered populations of earwigs of the genus Chelidura Latreille, 1825. There is some controversy about the specific assignment of these populations: while most authors assign them to C.
Pilar Jurado-Angulo +2 more
doaj +3 more sources
Linear codes resulting from finite group actions [PDF]
Transactions on Combinatorics, 2022 In this article, we use group action theory to define some important ternary linear codes. Some of these codes are self-orthogonal having a minimum distance achieving the lower bound in the previous records. Then, we define two new codes sharing the same
Driss Harzalla
doaj +1 more source
An algorithm for U–Pb geochronology by secondary ion mass spectrometry [PDF]
Geochronology, 2022 Secondary ion mass spectrometry (SIMS) is a widely used technique for in situ U–Pb geochronology of accessory minerals. Existing algorithms for SIMS data reduction and error propagation make a number of simplifying assumptions that degrade the precision
P. Vermeesch
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The Solution of some 100-city Travelling Salesman Problems
EURO Journal on Computational Optimization, 2021 A simplex-based FORTRAN code, working entirely in integer arithmetic, has been developed for the exact solution of travelling-salesman problems. The code adds tour-barring constraints as they are found to be violated.
A. Land
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Toward the Unification of Physics and Number Theory [PDF]
Reports in Advances of Physical Sciences, 2019 This paper introduces the notion of simplex-integers and shows how, in contrast to digital numbers, they are the most powerful numerical symbols that implicitly express the information of an integer and its set theoretic substructure.
Klee Irwin
doaj +1 more source