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A notion of multivariate BCH bounds and codes
2015
ACM Communications in Computer Algebra
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In this extended abstract, we use the techniques of computation of the minimum apparent distance of a hypermatrix given in [2] in order to develop a notion of BCH bound and BCH code in the multivariate ...
Keywords Minimum apparent distance of a hypermatrix, Apparent distance of an abelian code, Multivariable BCH bound, Multivarible BCH code. * This work was partially supported by MINECO (Ministerio de Economía ...
Camion [3] extended the study of the BCH bound to the family of abelian codes by introducing the notion of apparent distance of an abelian code. ...
doi:10.1145/2768577.2768597
fatcat:jj4lvm74gvfsnaf53wkncjylz4
Ds-bounds for cyclic codes: new bounds for abelian codes
[article]
2016
arXiv
pre-print
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In this paper we develop a technique to extend any bound for cyclic codes constructed from its defining sets (ds-bounds) to abelian (or multivariate) codes. ...
We use this technique to improve the searching of new bounds for abelian codes. ...
Conclusion We have developed a technique to extend any ds-bound for cyclic codes to multivariate codes which can be applied to codes of arbitrary length, mainly for those whose minimum distance is still ...
arXiv:1604.02949v1
fatcat:nw5fpmyy3fbl7cuws2tbfjdesq
From ds-bounds for cyclic codes to true distance for abelian codes
[article]
2017
arXiv
pre-print
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In this paper we develop a technique to extend any bound for the minimum distance of cyclic codes constructed from its defining sets (ds-bounds) to abelian (or multivariate) codes through the notion of ...
We also study conditions for an abelian code to verify that its B-apparent distance reaches its (true) minimum distance. Then we construct some tables of such codes as an application ...
X 2 ) = a(X 1 ) b(X 2 ), 7.1 Application 1: construction of abelian codes for which its multivariate BCH bound, apparent distance and minimum distance coincide. ...
arXiv:1704.03761v1
fatcat:2phfbt4kmnhmfexy7ji44rm6sy
Cyclic and BCH codes whose minimum distance equals their maximum BCH bound
2016
Advances in Mathematics of Communications
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To do this, we make use of two related tools: the discrete Fourier transform and the notion of apparent distance of a code, originally defined for multivariate abelian codes. 2010 Mathematics Subject Classification ...
We apply our results to the study of those BCH codes C, with designed distance δ, that have minimum distance d(C) = δ. ...
To solve our first problem, we make use of two related tools: the discrete Fourier transform and the notion of apparent distance of a code, originally defined for multivariate abelian codes in [1] . ...
doi:10.3934/amc.2016018
fatcat:kpevoe5r6vhp5g6qsxrv5qgtra
On the Shape of the General Error Locator Polynomial for Cyclic Codes
2017
IEEE Transactions on Information Theory
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The authors would like to thank Matteo Bonini and Michela Ceria for helpful suggestions and discussions. ...
ACKNOWLEDGEMENTS Most results in this paper are from the last author's PHD thesis and so she would like to thank her supervisor, the third author. ...
Remark 10: The apparently-trivial result ||a 1 +a 2 || = |a 1 + a 2 | in Theorem 9 is essential to show that our notion of functional density is meaningful. ...
doi:10.1109/tit.2017.2692213
fatcat:ieqpfa35qzayfpf2vc4kgwbpnm
Cyclic and convolutional codes with locality
[article]
2020
arXiv
pre-print
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As a result, we obtain a general family of hierarchical LRC codes for a new range of code parameters. ...
Among other results, we extend the general approach to cyclic codes with locality to multidimensional cyclic codes, yielding new families of LRC codes with availability, and construct a family of q-ary ...
Convolutional codes with row locality In this section we introduce and study another notion of locality for convolutional codes. ...
arXiv:2004.06770v1
fatcat:uzu2jxeo5zc7lj2dy5zimqokua
Estimating Cure Rates From Survival Data
2003
Journal of the American Statistical Association
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Notwithstanding the fact that the model has been around for less than a decade, a large body of theoretical results and applications has been reported to date. ...
This review article is intended to give a big picture of these modeling techniques and associated statistical problems. These issues are discussed in the context of survival data in cancer. ...
Acknowledgments The authors wish to thank the editor, the associate editor, and three referees for several suggestions and editorial changes which have greatly improved the paper. The research of A. ...
doi:10.1198/01622145030000001007
pmid:21151838
pmcid:PMC2998771
fatcat:3byf6lcynjhnndmvu6hgo6wyxi
Correcting errors and erasures via the syndrome variety
2005
Journal of Pure and Applied Algebra
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We propose a new syndrome variety, which can be used to decode cyclic codes. We present also a generalization to erasure and error decoding. ...
Assume G is a Gröbner basis for an ideal I ⊂ K[S, Z, T ], S = (s 1 , . . . , s H ), Z = (z 1 , . . . , z L ), T = (t 1 , . . . , t M ) w.r.t. a block order with S < Z < T and with the Z-variables ...
A special thank to Marc Giusti, for the use of the computational cluster MEDICIS. ...
doi:10.1016/j.jpaa.2004.12.027
fatcat:rqwepmil2vafdopuxxxlw24tva
Bacterial assemblages associated with coral species of the Mexican Central Pacific
2017
Revista de biologia marina y oceanografia
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The relationships between the bacterial-coral assemblage and environmental and spatial variables of the reef surroundings were also evaluated, using the multivariate analyses. ...
This study evaluated the bacteria associated with the mucus and tissues of Pocillopora damicornis and Pocillopora verrucosa, as well as that of the seawater and surrounding sediments, in 6 sites of the ...
Pablo Morales and Camila Fernández-Saez from the Laboratory of Environmental Microbiology in the University of Antofagasta for their advice in conducting the fingerprint profiling analyses. ...
doi:10.4067/s0718-19572017000200002
fatcat:3fhnzlobwzcgfidmvo5ajh4jca
Higher-Order MDS Codes
[article]
2021
arXiv
pre-print
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2021 pre-print arXiv:2111.03210v1 fatcat:efspaxi3jvdqvdorizzzxjlcrq
L-MDS codes are then defined as codes that attain this bound (under a slightly stronger notion of list decodability), with 1-MDS codes corresponding to ordinary linear MDS codes. ...
An improved Singleton-type upper bound is presented for the list decoding radius of linear codes, in terms of the code parameters [n,k,d] and the list size L. ...
However, this is absurd: there can be no |D ′ | ≤ 12 linearly dependent columns in the parity-check matrix of a binary BCH code whose minimum distance exceeds 12. ...
arXiv:2111.03210v2
fatcat:w2g6vkrarvdajbqt5ztkrpejci
Multiscale characteristics of the emerging global cryptocurrency market
[article]
2020
arXiv
pre-print
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The review introduces the history of cryptocurrencies, offering a description of the blockchain technology behind them. ...
Finally, an interesting observation on the Covid-19 pandemic impact on the cryptocurrency market is presented and discussed: recently we have witnessed a "phase transition" of the cryptocurrencies from ...
code (scripts) in a distributed form. ...
arXiv:2010.15403v1
fatcat:sgq6t2xg25cxtiy6exmqp7hnyi
Biometric Inspired Digital Image Steganography
2008
15th Annual IEEE International Conference and Workshop on the Engineering of Computer Based Systems (ecbs 2008)
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Steganography is defined as the science of hiding or embedding "data" in a transmission medium. ...
., against image processing and other attacks) and capacity of the hidden data (i.e., how much data we can hide in the carrier file), are the main factors that distinguish it from other "sisters-in science ...
Abdulaziz, and Pang [35] , use vector quantization called Linde-Buzo-Gray (LBG) coupled with Block codes known as BCH code and 1-Stage discrete Haar Wavelet transforms. ...
doi:10.1109/ecbs.2008.11
dblp:conf/ecbs/CheddadCCM08
fatcat:eyz2x6garnc3rpabw5nxcwbd2q
Post-Quantum Cryptography
[chapter]
2011
Encyclopedia of Cryptography and Security
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So, during one of the coffee breaks, we decided to edit a book on this subject. Springer-Verlag promptly agreed to publish such a volume. ...
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective ...
Acknowledgements We thank Phong Nguyen and Markus Rückert for helpful discussions on the practical security of lattice-based cryptography. ...
doi:10.1007/978-1-4419-5906-5_386
fatcat:ucdkilta7zc3voq7nqctmjkcr4
To gel or not to gel: correlating molecular gelation with solvent parameters
2015
Chemical Society Reviews
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Solvent parameters provide an understanding into the driving forces governing SAFiN formation aiding in the quest for a universal gelator. ...
RGW would like to acknowledge the National Science Foundation (Grant CHE-1147353) for its financial support of the research performed at Georgetown.
Notes and references ...
Acknowledgements MAR would like to acknowledge support from NSERC (371824-2009) entitled mechanisms of self-assembly in nanostructure edible oils. ...
doi:10.1039/c5cs00136f
pmid:25941907
fatcat:y3yu5lsgtffxpfvsguokzj2kxa
Synchronization over Cartan motion groups via contraction
[article]
2017
arXiv
pre-print
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Group contraction is an algebraic map that relates two classes of Lie groups by a limiting process. We utilize this notion for the compactification of the class of Cartan motion groups. ...
We thoroughly discuss the synchronization over this group and show numerically the advantages of our approach compared to some current state-of-the-art synchronization methods on both synthetic and real ...
on Algorithms and Geometry, and the Moore Foundation Data-Driven Discovery Investigator Award. ...
arXiv:1612.00059v3
fatcat:7w26vetzcreehmxaslwxxnbuai
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