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Two New Four-Error-Correcting Binary Codes

Patric R. J. Östergård
2005 Designs, Codes and Cryptography  
doi:10.1007/s10623-004-1723-3 fatcat:rlduredl2vh3zmbtlxueiawqhy

Geometric WOM codes and coding strategies for multilevel flash memories [article]

Kathryn Haymaker, Christine A. Kelley
2012 arXiv   pre-print
We also analyze methods of adapting binary WOM codes for use on multilevel flash cells. In particular, we give two strategies based on different rewrite objectives.  ...  This construction yields WOM codes with new parameters and provides insight into the criterion that incidence structures should satisfy to give rise to good codes.  ...  Acknowledgments Some of this work was completed while the authors were at the Fall 2011 program on Combinatorial, Algebraic and Algorithmic Aspects of Coding Theory at the Bernoulli Center, EPFL, Switzerland  ... 
arXiv:1206.5762v1 fatcat:fmm4tzcwrnd3fn7wxyq4ytzkim

A Review of design of Binary Golay Code and Extended Binary Golay Code for error correction

Mayanka Rai, Hema Singh
2018 International Journal of Trend in Scientific Research and Development  
The Golay code encodes 12-bits of data in such a way that it can correct 3-bits of error and detect 7-bits of error. G24 code is also called the Perfect Binary Golay Code.  ...  The two binary Golay codes formats are the Binary Golay Code (23-bit, G23) and Extended Binary Golay code (24-bit, G24).  ...  The binary Golay code (24, 12, 8) can be constructed as the direct sum of two array codes involving [6] four component codes, two of which are simple linear block codes and other two are symmetric code  ... 
doi:10.31142/ijtsrd11426 fatcat:d4h2ntcojfbnnhnuxdvr4ernea

Geometric WOM codes and coding strategies for multilevel flash memories

Kathryn Haymaker, Christine A. Kelley
2012 Designs, Codes and Cryptography  
We also analyze methods of adapting binary WOM codes for use on multilevel flash cells. In particular, we give two strategies based on different rewrite objectives.  ...  This construction yields WOM codes with new parameters and provides insight into the criterion that incidence structures should satisfy to give rise to good codes.  ...  Acknowledgments Some of this work was completed while the authors were at the Fall 2011 program on Combinatorial, Algebraic and Algorithmic Aspects of Coding Theory at the Bernoulli Center, EPFL, Switzerland  ... 
doi:10.1007/s10623-012-9681-7 fatcat:j3sp7tm5fvf55pmzbbp6wxlzom

The Performance of Concatenated Schemes Based on Non-binary Multithreshold Decoders [chapter]

Valery Zolotarev, Gennady Ovechkin, Pavel Ovechkin, Dina Satibaldina, Nurlan Tashatov
2014 Advances in Intelligent Systems and Computing  
The SER performance of qMTD is shown to be close to the results provided by optimum total search methods, which are not realizable for non-binary codes in general. qMTD decoders are compared with different  ...  decoders for Reed-Solomon and LDPC codes.  ...  In such systems to protect data from errors it is recommended to use non-binary error-correcting codes.  ... 
doi:10.1007/978-3-319-01857-7_24 fatcat:3w5444ani5hahfku2n74vsjwam

Page 4912 of Mathematical Reviews Vol. , Issue 94h [page]

1994 Mathematical Reviews  
Summary: “Binary block codes for correcting asymmetric errors are called binary AsEC block codes.  ...  (SF-TURK; Turku) Some features of binary block codes for correcting asymmetric errors.  ... 

Secret Key Distribution Protocol for Practical Optical Channels Using a Preshared Key and Phase Fluctuations

Tatsuya Tomaru
2010 Japanese Journal of Applied Physics  
Using the difference, new secret keys are generated information theoretically although a preshared key is used.  ...  The probabilistic property of signal-light fluctuations works with the preshared key to produce a difference in bit-error rate between a receiver and an eavesdropper.  ...  He decodes the binary signals to error-corrected signals based on the original function of the error-correcting code. Bob furthermore decodes them with SK2.  ... 
doi:10.1143/jjap.49.074401 fatcat:evit3nmf2jfp3pk4rz5xb3yehm

Trellis-coded modulation with redundant signal sets Part I: Introduction

G. Ungerboeck
1987 IEEE Communications Magazine  
As an illustration, consider four-phase modulation (4-PSK) without coding, and eight-phase modulation (8-PSK) used with a binary error-correction code of rate 2/3.  ...  Classical Error-Correction Coding In classical digital communication systems, the functions of modulation and error-correction coding are separated.  ... 
doi:10.1109/mcom.1987.1093542 fatcat:dqnpih5pibhovlfjwy2fydav3u

Page 59 of IBM Journal of Research and Development Vol. 4, Issue 1 [page]

1960 IBM Journal of Research and Development  
Specific applications of this class of codes are given for a modulation system where even errors only are ex- pected, and codes correcting two and four different types of related errors are described.  ...  Melas A New Group of Codes for Correction of Dependent Errors in Data Transmission Abstract: Multiple related errors of any configuration can be automatically corrected by a class of codes having the property  ... 

Two optimal one-error-correcting codes of length 13 that are not doubly shortened perfect codes

Patric R. J. Östergård, Olli Pottonen
2010 Designs, Codes and Cryptography  
Pottonen, The perfect binary one-error-correcting codes of length 15: Part I - Classification, IEEE Trans. Inform. Theory, to appear]; there are 117821 such (13,512,3) codes.  ...  By applying a switching operation to those codes, two more (13,512,3) codes are obtained, which are then not doubly shortened perfect codes.  ...  We shall here see that as a code switch maintains the minimum distance of the code, it is applicable to any error-correcting codes, not just perfect ones.  ... 
doi:10.1007/s10623-010-9450-4 fatcat:tnkrlcmwkjeslnbopsufikpmmm

Modelling the Storage Capacity of 2d Pixel Mosaics [chapter]

Simone Göttlich, Thorsten Sickenberger
2011 Real-World Problems for Secondary School Mathematics Students  
The binary message produced is now coded through an error correction process.  ...  Note that for the QR Code, the Reed-Solomon error correction is being used. This algorithm divides the binary message into units of 8 Bits each and calculates their error correction information.  ... 
doi:10.1007/978-94-6091-543-7_5 fatcat:a66hbsxzbzh2hottnmvcs5s7ii

Separability of ternary Error-Correcting Output Codes

Sergio Escalera, Oriol Pujol, Petia Radeva
2008 Pattern Recognition (ICPR), Proceedings of the International Conference on  
Error Correcting Output Codes (ECOC) represent a successful framework to deal with multi-class categorization problems based on combining binary classifiers.  ...  In this paper, we present a new formulation of the ternary ECOC distance and the error-correcting capabilities in the ternary ECOC framework.  ...  Based on the new measure and the ternary error-correcting capabilities, we propose a new sparse coding design.  ... 
doi:10.1109/icpr.2008.4761048 dblp:conf/icpr/EscaleraPR08 fatcat:ish4zvy5ejhpldgravpvvbqk2q

Page 545 of Communications of the Association for Computing Machinery Vol. 4, Issue 12 [page]

1961 Communications of the Association for Computing Machinery  
The paper introduces a new family of codes for detecting and correcting multiple errors in a binary-coded message.  ...  A four-dimensional code, correcting three and detecting four errors, has been developed; the extension to higher-dimensional codes with greater correction power is straightforward. l.  ... 

On multiple insertion/deletion correcting codes

A.S.J. Helberg, H.C. Ferreira
2002 IEEE Transactions on Information Theory  
We investigate binary, number-theoretic, bit insertion/deletion correcting codes as pioneered by Levenshtein.  ...  The weight spectra and Hamming distance properties of single insertion/deletion error-correcting codes are analyzed.  ...  In [1] , some characteristics of binary codes that can correct insertions, deletions, and additive errors are given, as well as two single-error correcting classes of codes.  ... 
doi:10.1109/18.971760 fatcat:3axt3lo3tjf6pglfennpp7rabu

On Step-by-Step Complete Decoding Triple-Error-Correcting Binary BCH Codes

S.-W. WEI
2006 IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences  
According to the properties found in the algebraic complete decoding method for triple-error-correcting binary Bose-Chaudhuri-Hocquenghem (BCH) codes, a step-by-step complete decoding algorithm of this  ...  code is presented.  ...  Triple-Error-Correcting Binary BCH Codes It had been proven that the triple-error-correcting binary BCH codes can correct some patterns of four and five errors if beyond BCH bound decoding is employed  ... 
doi:10.1093/ietfec/e89-a.11.3360 fatcat:xw5y77ezvvehdlril6nkfwhyli
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