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Improved lower bounds on sizes of single-error correcting codes

Simon Litsyn, Beniamin Mounits
2006 Designs, Codes and Cryptography  
Substitution of the derived codes into a concatenation construction yields nonlinear binary single-error correcting codes with better than known parameters.  ...  In particular, new binary single-error correcting codes having more codewords than the best previously known in the range n ≤ 512 are obtained for the lengths 64-66, 128-133, 256-262, and 512.  ...  In Sect. 3, we apply the new construction and obtain improved lower bounds on A(n, 3). The following notations will be used.  ... 
doi:10.1007/s10623-006-9015-8 fatcat:o4yt4el34bca3cv4sc6lv7c6nm

Two-Dimensional Cluster-Correcting Codes

M. Schwartz, T. Etzion
2005 IEEE Transactions on Information Theory  
We consider two-dimensional error-correcting codes capable of correcting a single arbitrary cluster of errors of size .  ...  We also construct 3-cluster-correcting codes and -straight-cluster-correcting codes. We conclude by improving the Reiger bound for two-dimensional cluster-correcting codes.  ...  The authors also wish to thank the anonymous reviewers, whose comments improved the presentation of the paper.  ... 
doi:10.1109/tit.2005.847726 fatcat:dch6u6hsbjcmnddfzvkp7wauvu

Correcting Grain-Errors in Magnetic Media

Ryan Gabrys, Eitan Yaakobi, Lara Dolecek
2015 IEEE Transactions on Information Theory  
Using this insight, new bounds on the maximum cardinality of a grain-error correcting code are derived and constructions of codes that correct grain-errors are considered.  ...  It is also demonstrated that permutations of the classical group codes can correct a single grain-error.  ...  ACKNOWLEDGEMENTS The authors would like to thank Artyom Sharov for his helpful discussions about code cardinalities and Enoch Andersson for his assistance with simulations.  ... 
doi:10.1109/tit.2015.2409860 fatcat:rk53pt65wfhttjodiu3w4rhhbq

Correcting grain-errors in magnetic media

Ryan Gabrys, Eitan Yaakobi, Lara Dolecek
2013 2013 IEEE International Symposium on Information Theory  
Using this insight, new bounds on the maximum cardinality of a grain-error correcting code are derived and constructions of codes that correct grain-errors are considered.  ...  It is also demonstrated that permutations of the classical group codes can correct a single grain-error.  ...  ACKNOWLEDGEMENTS The authors would like to thank Artyom Sharov for his helpful discussions about code cardinalities and Enoch Andersson for his assistance with simulations.  ... 
doi:10.1109/isit.2013.6620314 dblp:conf/isit/GabrysYD13 fatcat:qo3ej7oumrfgpp6mpurgljlosa

Page 1454 of Mathematical Reviews Vol. 44, Issue 6 [page]

1972 Mathematical Reviews  
Math. 17 (1969), 1311-1316; MR 42 #5817], the authors give improved upper bounds on o(n, m) for n =m, and improved lower bounds on p(n, m).  ...  Let y(n, m) be the maximum size of any such single-error-correcting code and o(n, m) the minimum size of any such covering set. Extending results of their earlier papers [the authors, J. London Math.  ... 

Integer codes and lattice packings by cubes of sidelength k

Ulrich Tamm
2015 2015 Information Theory and Applications Workshop (ITA)  
For side length greater 3 the equivalence of single error correcting integer codes and zero-error codes does not hold any more.  ...  For an asymmetric error of size one these cubes have side length 2 and the problem can be shown to be equivalent to finding zero-error codes for cycles in the sense of Shannon and Lovasz.  ...  Lovasz' famous bound via algebraic graph theory for odd cycles, hence, also yields an upper bound on the size of integer codes correcting a single asymmetric error.  ... 
doi:10.1109/ita.2015.7308983 dblp:conf/ita/Tamm15 fatcat:ouco2m6i7rfx5ivjlrev7ekia4

Correcting Grain-Errors in Magnetic Media [article]

Ryan Gabrys, Eitan Yaakobi, Lara Dolecek
2018 arXiv   pre-print
We derive new bounds on the maximum cardinality of a grain-error-correcting code and propose constructions of codes that correct grain-errors.  ...  We demonstrate that a permutation of the classical group codes (e.g., Constantin-Rao codes) can correct a single grain-error.  ...  ACKNOWLEDGEMENTS The authors would like to thank Artyom Sharov for his helpful discussions about code cardinalities as well as Associate Editor Prof.  ... 
arXiv:1307.7087v2 fatcat:qx36xaopfzf5ror64kpm3cps5a

The Error-Pattern-Correcting Turbo Equalizer: Spectrum Thinning at High SNRs

Hakim Alhussien, Jaekyun Moon
2011 IEEE Transactions on Information Theory  
The error-pattern correcting code (EPCC) is incorporated in the design of a turbo equalizer (TE) with aim to correct dominant error events of the inter-symbol interference (ISI) channel at the output of  ...  correcting code (TE-EPCC) exhibits a much lower bit-error rate (BER) floor compared to the conventional non-precoded TE, especially for high rate applications.  ...  This increases the code rate and codeword length, and also improves the single-error-pattern correction accuracy.  ... 
doi:10.1109/tit.2010.2096031 fatcat:kfu4zcsopff6vcevk7y5435oeq

A note on the size of N-free families [article]

Ryan R. Martin, Shanise Walker
2017 arXiv   pre-print
Katona and Tarján proved that La(n,N)≥n k+A(n,4,k+1), where k= n/2 and A(n, 4, k+1) is the size of a single-error-correcting code with constant weight k+1.  ...  In this note, we prove for n even and k=n/2, La(n, N) ≥n k+A(n, 4, k), which improves the bound on La(n, N) in the second order term for some values of n and should be an improvement for an infinite family  ...  The quantity A(n, 2δ, k) is important in the field of error-correcting codes. In fact, A(n, 4, k) computes the size of a single-error-correcting code with constant weight k.  ... 
arXiv:1609.02442v2 fatcat:q27y4g4ijja73nqni5rcnyfguu

A Novel Variation Operator for More Rapid Evolution of DNA Error Correcting Codes

D. Ashlock, S.K. Houghten
2005 2005 IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology  
Error correcting codes over the edit metric have been used as embedded DNA markers in at least one sequencing project.  ...  Presented here is an substantially faster evolutionary algorithm for locating error correcting codes over the edit metric that exhibits either equivalent or only slightly inferior performance on test cases  ...  Table I , which gives the sizes of the (n, d)-Conway codes, serves as a lower bound on the size of the sets of words we will need to specify.  ... 
doi:10.1109/cibcb.2005.1594898 fatcat:gyci2jnq2vcetdmakwqajo6p44

Bounds on the Size of Permutation Codes with the Kendall τ-Metric [article]

Sarit Buzaglo, Tuvi Etzion
2022 arXiv   pre-print
We prove that there are no perfect single-error-correcting codes in S_n, where n>4 is a prime or 4≤ n≤ 10. We present lower bounds on the size of optimal anticodes with odd diameter.  ...  As a consequence we obtain a new upper bound on the size of codes in S_n with even minimum Kendall τ-distance. We present larger single-error-correcting codes than the known ones in S_5 and S_7.  ...  Two large single-error-correcting codes for n = 5 and n = 7 are constructed in this way and yield an improvement on the related lower bounds.  ... 
arXiv:1408.4963v3 fatcat:b6zmskuosjgwvhdqnx6brw5rya

On network-error correcting convolutional codes under the BSC edge error model

K. Prasad, B. Sundar Rajan
2010 2010 IEEE International Symposium on Information Theory  
We derive a lower bound on the slope of any rate b/c convolutional code with a certain degree.  ...  Convolutional network-error correcting codes (CNECCs) are known to provide error correcting capability in acyclic instantaneous networks within the network coding paradigm under small field size conditions  ...  Moreover, the bound increases with the size of the network. It is therefore necessary to study network-error correcting codes which work under small field size conditions.  ... 
doi:10.1109/isit.2010.5513774 dblp:conf/isit/PrasadR10 fatcat:5e6j3vb5cva2zfdtsysea3cdty

Estimating the size of correcting codes using extremal graph problems [chapter]

Sergiy Butenko, Panos Pardalos, Ivan Sergienko, Vladimir Shylo, Petro Stetsyuk
2009 Springer Optimization and Its Applications  
Finding estimates of the size of correcting codes is important from both theoretical and practical perspectives.  ...  We solve the problem of finding the largest correcting codes using previously developed algorithms for optimization problems in graphs. We report new exact solutions and estimates.  ...  As a result, some improved lower bounds and exact solutions for the size of largest error-correcting codes were obtained.  ... 
doi:10.1007/978-0-387-98096-6_12 fatcat:gatotxuh5neljgrapds643zs6u

New single asymmetric error-correcting codes

S. Al-Bassam, R. Venkatesan, S. Al-Muhammadi
1997 IEEE Transactions on Information Theory  
New single asymmetric error-correcting codes are proposed. These codes are better than existing codes when the code length n is greater than 10, except for n = 12 and n = 15.  ...  It should be noted that the proposed codes for n = 12 and n = 15 are also the best known codes that can be explicitly constructed, since the best of the existing codes for these values of n are based on  ...  Thanks are also due to the anonymous referee whose queries and suggestions have improved this correspondence.  ... 
doi:10.1109/18.623162 fatcat:6qrsu75bjrfptgac2vqux65uyq

Guest Editorial Special Issue: "From Deletion-Correction to Graph Reconstruction: In Memory of Vladimir I. Levenshtein"

Alexander Barg, Lara Dolecek, Ryan Gabrys, Gyula O. H. Katona, János Körner, Andrew McGregor, Olgica Milenkovic, Sihem Mesnager, Gilles Zémor
2021 IEEE Transactions on Information Theory  
The authors provide new bounds on the size of the list and improve upon existing work in this area.  ...  minimum and maximum distances, as well as universal lower bounds on the potential energy of codes with a given maximum distance and cardinality.  ... 
doi:10.1109/tit.2021.3072555 dblp:journals/tit/BargDGKKMMMZ21 fatcat:ebzt3z72yjfwtbiqczqjqzwzk4
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