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A notion of multivariate BCH bounds and codes

José Joaquín Bernal, Juan Jacobo Simón, Diana H. Bueno-Carreño
2015 ACM Communications in Computer Algebra  
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]

J. J. Bernal, M. Guerreiro, J. J. Simón
2016 arXiv   pre-print
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]

J. J. Bernal, M. Guerreiro, J. J. Simón
2017 arXiv   pre-print
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

José Joaquín Bernal, Diana H. Bueno-Carreño, Juan Jacobo Simón
2016 Advances in Mathematics of Communications  
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

Fabrizio Caruso, Emmanuela Orsini, Massimiliano Sala, Claudia Tinnirello
2017 IEEE Transactions on Information Theory  
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]

Zitan Chen, Alexander Barg
2020 arXiv   pre-print
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

A. D Tsodikov, J. G Ibrahim, A. Y Yakovlev
2003 Journal of the American Statistical Association  
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

Emmanuela Orsini, Massimiliano Sala
2005 Journal of Pure and Applied Algebra  
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

Joicye Hernández-Zulueta, Leopoldo Díaz-Pérez, Rubén Araya, Ofelia Vargas-Ponce, Alma P Rodríguez-Troncoso, Eduardo Ríos-Jara, Marco Ortiz, Fabián A Rodríguez-Zaragoza
2017 Revista de biologia marina y oceanografia  
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]

Ron M. Roth
2021 arXiv   pre-print
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]

Marcin Wątorek, Stanisław Drożdż, Jarosław Kwapień, Ludovico Minati, Paweł Oświęcimka, Marek Stanuszek
2020 arXiv   pre-print
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

Abbas Cheddad, Joan Condell, Kevin Curran, Paul Mc Kevitt
2008 15th Annual IEEE International Conference and Workshop on the Engineering of Computer Based Systems (ecbs 2008)  
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]

Qijun Gu, Pascal Paillier, Tanja Lange, Edlyn Teske, Darrel Hankerson, Alfred Menezes, David Zhang, Feng Yue, Wangmeng Zuo, Jean-Jacques Quisquater, Gildas Avoine, Gerald Brose (+73 others)
2011 Encyclopedia of Cryptography and Security  
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

Y. Lan, M. G. Corradini, R. G. Weiss, S. R. Raghavan, M. A. Rogers
2015 Chemical Society Reviews  
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]

Onur Ozyesil, Nir Sharon, Amit Singer
2017 arXiv   pre-print
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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