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Labelings of Lee and Hamming spaces

Marcelo Muniz, Sueli I.R. Costa
2003 Discrete Mathematics  
Labelings of general Hamming spaces and of Reed-Muller codes RM(1; m) are characterized here in the context of isometry groups.  ...  The labeling of the Hamming Space (Z 2 2 ; d h ) by the rotation group Z4 and its coordinate-wise extension to Z 2n 2 give rise to the concept of Z4-linearity.  ...  Barros and Edson Agustini for important comments and technical support, and the referees for valuable suggestions.  ... 
doi:10.1016/s0012-365x(02)00454-5 fatcat:i4ryatyelvavjdrt2zbdoftglu

Page 9830 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
The concept of Z,-linearity can be seen as a labeling relation between the Lee space (Z4, dice) and the Hamming space (Z3,dn), where dj. and d;, denote the Lee metric and the Hamming metric, respectively  ...  In this paper, labelings of Lee and Hamming spaces are studied using a metric graph on quotient spaces approach via symmetry groups.  ... 

Optimal self-dual codes over Z4

Eric Rains
1999 Discrete Mathematics  
The optimal minimal Euclidean norm of self-dual codes over Z4 is known through length 24; the purpose of the present note is to determine the optimal minimal Hamming and Lee weights in this range.  ...  In the process, we classify all Lee-optimal codes of length 18, 21, 23, and 24.  ...  The optimal Lee weight of a self-dual code of length 18 through 24 is 8; 6; 8; 8; 8; 10; and 12; respectively. A self-dual code of length 21 or 22 is Lee-optimal if and only if it is Hamming-optimal.  ... 
doi:10.1016/s0012-365x(98)00358-6 fatcat:fdq3mvxd3rfsbpwnuil4hpd6pm

Compact Multi-Label Learning

Xiaobo Shen, Weiwei Liu, Ivor Tsang, Quan-Sen Sun, Yew-Soon Ong
CoH first regards the input and output as two views, and then aims to learn a common latent hamming space, where input and output pairs are compressed into compact binary embeddings.  ...  CoH enjoys two key benefits: 1) the input and output can be well aligned, and their correlations are explored; 2) the prediction is very efficient using fast cross-view kNN search in the hamming space.  ...  Acknowledgments This research is supported by the National Science Foundation of China (Grant No. 61273251, 61673220), the ARC Future Fellowship FT130100746, ARC grant LP150100671, DP180100106, and partially  ... 
doi:10.1609/aaai.v32i1.11708 fatcat:tgwgj3te6jgctpj6zx7yuobtky

Relating propelinear and binary G-linear codes

Marcelo M.S. Alves, João R. Gerônimo, Reginaldo Palazzo, Sueli I.R. Costa, J.Carmelo Interlando, Martinho C. Araújo
2002 Discrete Mathematics  
In this paper we establish the connections between two di erent extensions of Z4-linearity for binary Hamming spaces.  ...  We present both notions -propelinearity and G-linearity -in the context of isometries and group actions, taking the viewpoint of geometrically uniform codes extended to discrete spaces.  ...  Acknowledgements The authors are grateful to the referee for valuable comments and suggestions.  ... 
doi:10.1016/s0012-365x(01)00206-0 fatcat:vo3tapa3kzcchol3zts73mjpua

Information Theoretic Feature Selection in Multi-label Data through Composite Likelihood [chapter]

Konstantinos Sechidis, Nikolaos Nikolaou, Gavin Brown
2014 Lecture Notes in Computer Science  
Furthermore we can derive new problem-specific criteria by making different independence assumptions over the feature and label spaces.  ...  Our framework combines two different ideas; expressing multi-label decomposition methods as composite likelihoods and then showing how feature selection criteria can be derived by maximizing these likelihood  ...  Sechidis gratefully acknowledges the support of the Propondis Foundation.  ... 
doi:10.1007/978-3-662-44415-3_15 fatcat:6wgyrndnxrbgxdkzbnzj6ruamq

Block-coded PSK modulation using two-level group codes over dihedral groups

J. Bali, B.S. Rajan
1998 IEEE Transactions on Information Theory  
It is shown that depending upon the ratio of Hamming distances of the component codes some labelings perform better than other. The best labeling is identified under a set of restrictive conditions.  ...  Using two-level group codes over D M as label codes, performance of block-coded modulation scheme is discussed under all possible matched labelings of 2M-APSK and 2M-SPSK (asymmetric and symmetric PSK)  ...  Kschischang, and R. Garello for sending the preprints of their work and the anonymous reviewers whose suggestions greatly improved the clarity of presentation.  ... 
doi:10.1109/18.681341 fatcat:i5vxgxiskreojmxgzusldzryia

The Nordstrom-Robinson code is the binary image of the octacode [chapter]

G Forney, Neil Sloane, M Trott
1993 Coding and Quantization  
The Nordstrom-Robinson code, a nonlinear binary code of length 16 and minimal Hamming distance 6, is the binary image of the octacode, a linear self-dual code over 4 of length 8 and minimal Lee distance  ...  Since the octacode is the 4 -analogue of a Hamming code, this provides an extremely simple definition of the Nordstrom-Robinson code.  ...  The transformation ρ now becomes a 90 • rotation in 2-space, Lee distance becomes Euclidean distance, and the image of a linear code over 4 becomes a geometrically uniform subset of the hypercube in Euclidean  ... 
doi:10.1090/dimacs/014/03 dblp:conf/dimacs/ForneyST92 fatcat:qssfn4hujzavro2nnsyt7pk33i

Page 120 of Entomological News Vol. 22, Issue 3 [page]

1911 Entomological News  
, reaching nearly, or quite to the sub- apical fascia; the apex is black (pale in most specimens of rosmarus) and the black space intervening between the pale  ...  This specimen is from the “Pea¬ body colln.” and bears the locality label “Ut.” and the name label analis, from which it is entirely distinct. Enoclerus opifex Gorh., Biol. Centr.  ... 

MUTE: Data-Similarity Driven Multi-hot Target Encoding for Neural Network Design [article]

Mayoore S. Jaiswal, Bumsoo Kang, Jinho Lee, Minsik Cho
2019 arXiv   pre-print
In this paper, we present a novel and efficient target encoding scheme, MUTE to improve both generalizability and robustness of a target model by understanding the inter-class characteristics of a target  ...  By extracting the confusion level between the target classes in a dataset, MUTE strategically optimizes the Hamming distances among target encoding.  ...  further apart in the label space in terms of the Hamming distance.  ... 
arXiv:1910.07042v1 fatcat:zlmpo6ukq5e45owivlhjapseri

Locality-Sensitive Hashing Techniques for Nearest Neighbor Search

Keon Myung Lee
2012 International Journal of Fuzzy Logic and Intelligent Systems  
This paper introduces the notion of locality-sensitive hashing and surveys the locality-sensitive hashing techniques.  ...  It categories them based on several criteria, presents their characteristics, and compares their performance.  ...  The hash codes are here binary codes, the buckets are labeled by the binary hash codes, and Hamming distances between buckets reflect the similarity of data from the buckets.  ... 
doi:10.5391/ijfis.2012.12.4.300 fatcat:qwkw27hpd5ht5jhzwfgcajyfs4

A PSO-based multi-objective multi-label feature selection method in classification

Yong Zhang, Dun-wei Gong, Xiao-yan Sun, Yi-nan Guo
2017 Scientific Reports  
Moreover, the idea of the archive, and the crowding distance are applied to PSO for finding the Pareto set.  ...  exploit the areas with sparse solutions in the search space.  ...  To overcome this drawback, Lee and Kim presented a memetic-based multi-label feature selection algorithm 22 .  ... 
doi:10.1038/s41598-017-00416-0 pmid:28336938 pmcid:PMC5428503 fatcat:thzqcymvsfgy3hkhau7frfmd74

FSL-BM: Fuzzy Supervised Learning with Binary Meta-Feature for Classification [article]

Kamran Kowsari, Nima Bari, Roman Vichr, Farhad A. Goodarzi
2017 arXiv   pre-print
While many studies focused on reducing time complexity and increasing accuracy during the last decade, the novel contribution of this proposed solution comes through integration of Hamming Distance, Hash  ...  To summarize, the main contribution of this technique for real-time Fuzzy Supervised Learning is to represent hypothesis through binary input as meta-feature space and creating the Fuzzy Supervised Hash  ...  percents to label −1 and 80% belongs to label +1 .  ... 
arXiv:1709.09268v1 fatcat:qnx665p3gncoleqchyzp65ph4q

Page 363 of Mathematical Reviews Vol. 56, Issue 1 [page]

1978 Mathematical Reviews  
Using Lee distance instead of Hamming distance, the authors derive a lower bound for the number of parity checks necessary for correcting errors of Lee weight e or less, and bursts of length bor less with  ...  Upper and lower bounds on the p be: labele infor check has © comp and | (1967 may Per nHzs  ... 

Codes, Correlations and Power Control in OFDM [chapter]

James A. Davis, Jonathan Jedwab, Kenneth G. Paterson
1999 Difference Sets, Sequences and their Correlation Properties  
However, the interaction between theory and practice is a two-way process: the application motivates further study of a fertile interplay between coding theory, graph theory and sequence design.  ...  Firstly we study polyphase Golay sequences, motivating the introduction of non-binary generalisations of the Reed-Muller codes.  ...  Acknowledgements The first author thanks Hewlett-Packard for generous support during the time of this research.  ... 
doi:10.1007/978-94-011-4459-9_5 fatcat:73emoqrctvb5vcy7d6ijlamnzq
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