Filters








329,348 Hits in 7.0 sec

A family of codes with locality containing optimal codes

Bruno Andrade, Cicero Carvalho, Victor G. L. Neumann, Antonio C.P. Veiga.
<span title="">2022</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q7qi7j4ckfac7ehf3mjbso4hne" style="color: black;">IEEE Access</a> </i> &nbsp;
In this work we introduce a new family of codes with locality, which are subcodes of a certain family of evaluation codes.  ...  Locally recoverable codes were introduced by Gopalan et al. in 2012, and in the same year Prakash et al. introduced the concept of codes with locality, which are a type of locally recoverable codes.  ...  A FAMILY OF LOCALLY RECOVERABLE CODES Let F q be a finite field with q elements. Definition 2.1: Let m, r, δ be positive integers, with δ ≥ 2 and r +δ−1 ≤ m.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/access.2022.3165032">doi:10.1109/access.2022.3165032</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sz4usgomgbf5thkax2jxcyfo6y">fatcat:sz4usgomgbf5thkax2jxcyfo6y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220521094131/https://ieeexplore.ieee.org/ielx7/6287639/9668973/09749211.pdf?tp=&amp;arnumber=9749211&amp;isnumber=9668973&amp;ref=" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f8/43/f8435a9730bea309f841116e6f2bcac14866c1d4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/access.2022.3165032"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> ieee.com </button> </a>

A family of codes with locality containing optimal codes [article]

Bruno Andrade, Cícero Carvalho, Victor G.L. Neumann, Antônio C.P. Veiga
<span title="2021-01-19">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this work we introduce a new family of codes with locality, which are subcodes of a certain family of evaluation codes.  ...  Locally recoverable codes were introduced by Gopalan et al. in 2012, and in the same year Prakash et al. introduced the concept of codes with locality, which are a type of locally recoverable codes.  ...  In this paper we define a family consisting of subcodes of the so-called affine cartesian codes (see Definition 2.2) which are (r, δ)-locally recoverable codes.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2101.07629v1">arXiv:2101.07629v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zvmjsns3urcb7jlkqqtbwlhp3m">fatcat:zvmjsns3urcb7jlkqqtbwlhp3m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210128141315/https://arxiv.org/pdf/2101.07629v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9f/d0/9fd0866a6119da0da527fc3f90d0e59f0f570bb4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2101.07629v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Local-Optimality Guarantees for Optimal Decoding Based on Paths [article]

Guy Even, Nissim Halabi
<span title="2012-08-14">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We apply the technique of local-optimality to a family of Tanner codes.  ...  This paper presents a unified analysis framework that captures recent advances in the study of local-optimality characterizations for codes on graphs.  ...  We apply the proof technique to a family of codes, called even Tanner codes, that contains repeat accumulate codes with a even repetition factors, LDPC codes with even left degrees, and expander codes  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1203.1854v2">arXiv:1203.1854v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tulfwhpf4rfbdjdchhb362mmba">fatcat:tulfwhpf4rfbdjdchhb362mmba</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1203.1854/1203.1854.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1203.1854v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Cyclic and convolutional codes with locality [article]

Zitan Chen, Alexander Barg
<span title="2020-04-14">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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  ...  As a result, we obtain a general family of hierarchical LRC codes for a new range of code parameters.  ...  A family of tailbiting convolutional codes with row locality We come to the main result of this section, which is a construction of a family of convolutional codes with pr, δq row locality.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2004.06770v1">arXiv:2004.06770v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uzu2jxeo5zc7lj2dy5zimqokua">fatcat:uzu2jxeo5zc7lj2dy5zimqokua</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200417221957/https://arxiv.org/pdf/2004.06770v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2004.06770v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Optimal Binary Locally Repairable Codes via Anticodes [article]

Natalia Silberstein, Alexander Zeh
<span title="2015-01-28">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This paper presents a construction for several families of optimal binary locally repairable codes (LRCs) with small locality (2 and 3). This construction is based on various anticodes.  ...  Moreover, most of these codes are optimal with respect to the Griesmer bound.  ...  Besides the optimality with respect to the Cadambe-Mazumdar bound for a given locality, several of our families of codes fulfill the Griesmer bound with equality.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1501.07114v1">arXiv:1501.07114v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/izkmwqxkjzdxjh2wodaplnlscy">fatcat:izkmwqxkjzdxjh2wodaplnlscy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200829002751/https://arxiv.org/pdf/1501.07114v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6e/cd/6ecd0265262221a17ea05e07ed3ebabea611c169.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1501.07114v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Binary cyclic codes that are locally repairable

Sreechakra Goparaju, Robert Calderbank
<span title="">2014</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ux5tf45dtrgptnezraiii73msm" style="color: black;">2014 IEEE International Symposium on Information Theory</a> </i> &nbsp;
To this end, we construct new families of binary linear codes that have an optimal dimension (rate) for a given minimum distance and locality.  ...  In doing so, we discover new upper bounds on the code dimension, and prove the optimality of enabling local repair by provisioning disjoint groups of disks.  ...  a family of Singleton-optimal codes 4 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isit.2014.6874918">doi:10.1109/isit.2014.6874918</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/isit/GoparajuC14.html">dblp:conf/isit/GoparajuC14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ijxy3ghsmbcahh4bo22zzasfeu">fatcat:ijxy3ghsmbcahh4bo22zzasfeu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200916014839/https://arxiv.org/pdf/1609.08935v1.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/94/c2/94c2d979c77092a6f4d152369dd69271c6342a41.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isit.2014.6874918"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

The minimum linear locality of linear codes [article]

Pan Tan, Cuiling Fan, Cunsheng Ding, Zhengchun Zhou
<span title="2021-02-01">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The minimum linear locality of many families of linear codes are settled with the general theory developed in this paper.  ...  Motivated by these two facts, this paper develops some general theory about the minimum linear locality of linear codes, and investigates the minimum linear locality of a number of families of linear codes  ...  Notice that the two theorems above provide not only two families of d-optimal and k-optimal LLRCs, but also two families of NMDS codes with new parameters. D.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2102.00597v1">arXiv:2102.00597v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iu5eoxpcjbea7bptnueoc6ryx4">fatcat:iu5eoxpcjbea7bptnueoc6ryx4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210207135112/https://arxiv.org/pdf/2102.00597v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/aa/20/aa20e8858f4845f9a6d20afeaa18609842a2a3a2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2102.00597v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Optimal Locally Repairable Codes and Connections to Matroid Theory [article]

Itzhak Tamo, Dimitris S. Papailiopoulos, Alexandros G. Dimakis
<span title="2013-01-31">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Locally Repairable Codes (LRCs) form a new family of codes that are repair efficient.  ...  For the analysis of the optimality of the code, we derive a new result on the matroid represented by the code generator matrix.  ...  Codes with all-symbol locality that meet the above bound are termed optimal LRCs and are known to exist when (r + As of now, designing LRCs with optimal distance for most code parameters n, k, r that are  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1301.7693v1">arXiv:1301.7693v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yztqsmgvxjdm3ans2pmk7wsbwi">fatcat:yztqsmgvxjdm3ans2pmk7wsbwi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200907030912/https://arxiv.org/pdf/1301.7693v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7a/01/7a01c284d2dcc4830e8c597c1b67862b5f1d5b8b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1301.7693v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Bounds and constructions of codes with multiple localities

Alexander Zeh, Eitan Yaakobi
<span title="">2016</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ux5tf45dtrgptnezraiii73msm" style="color: black;">2016 IEEE International Symposium on Information Theory (ISIT)</a> </i> &nbsp;
We give a family of binary ML-LRCs based on generalized code concatenation that is optimal with respect to the alphabet-dependent bound.  ...  In the simplest case of two localities some code symbols of an ML-LRC have a certain locality while the remaining code symbols have another one.  ...  Section V contains a family of r-local binary LRCs based on generalized code concatenation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isit.2016.7541377">doi:10.1109/isit.2016.7541377</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/isit/ZehY16.html">dblp:conf/isit/ZehY16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/shljnhm4fvcdnlmn42mzfonpga">fatcat:shljnhm4fvcdnlmn42mzfonpga</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190502180212/https://hal.inria.fr/hal-01253384/file/ML-LRC.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/12/ae/12ae2ff9c246b446b99e0e5186ee869feadd0ff2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isit.2016.7541377"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Bounds and Constructions of Codes with Multiple Localities [article]

Alexander Zeh, Eitan Yaakobi
<span title="2016-01-12">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We give a family of binary ML-LRCs based on generalized code concatenation that is optimal with respect to the alphabet-dependent bound.  ...  In the simplest case of two localities some code symbols of an ML-LRC have a certain locality while the remaining code symbols have another one.  ...  Section V contains a family of r-local binary LRCs based on generalized code concatenation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1601.02763v1">arXiv:1601.02763v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d4zrypona5dx7mipq6w6v2g3ly">fatcat:d4zrypona5dx7mipq6w6v2g3ly</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191013082015/https://arxiv.org/pdf/1601.02763v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b4/62/b46233c2b3a89dcfd2001f4093e70665c888937a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1601.02763v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Cyclic linear binary locally repairable codes

Pengfei Huang, Eitan Yaakobi, Hironori Uchikawa, Paul H. Siegel
<span title="">2015</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jyfj6ubbwzcqdb2m3vg7epe6tu" style="color: black;">2015 IEEE Information Theory Workshop (ITW)</a> </i> &nbsp;
Using this result, we investigate the locality of a variety of well known cyclic linear binary codes, e.g., Hamming codes and Simplex codes, and also prove their optimality with our improved bound for  ...  Several families of such modified codes are considered and their optimality is addressed. Finally, we investigate the locality of Reed-Muller codes.  ...  Let us first show that the bound (2) can be improved for the family of linear codes with all symbol locality.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/itw.2015.7133128">doi:10.1109/itw.2015.7133128</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/itw/HuangYUS15.html">dblp:conf/itw/HuangYUS15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vqnmhf5g3rhzjnahyec3ln73je">fatcat:vqnmhf5g3rhzjnahyec3ln73je</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200321001046/http://cmrr-star.ucsd.edu/static/pubs/lrc_itw2015.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/74/fd/74fd27cddd52c6eef6232dd9146d094f613962bb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/itw.2015.7133128"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

ON THE COMPILATION OF A LANGUAGE FOR GENERAL CONCURRENT TARGET ARCHITECTURES

THOMAS A.M. BERNARD, CLEMENS GRELCK, CHRIS R. JESSHOPE
<span title="">2010</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/x6p3xmf7graczk5begbrisonce" style="color: black;">Parallel Processing Letters</a> </i> &nbsp;
In this paper, we present compilation schemes for a general model of concurrency captured in a parallel language designed for system-level programming and as a target for higher level compilers.  ...  We also expose the challenges of integrating these transformation rules into a sequential-oriented compiler. Moreover, we discuss resource mapping inherent to those challenges.  ...  Acknowledgements The SVP model and its implementation is a group effort and the authors would like to thank all members of the Computer Systems Architecture group for their input to this work: Mike Lankamp  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0129626410000053">doi:10.1142/s0129626410000053</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hqps4sosfbgtddvst6mpb7p7ny">fatcat:hqps4sosfbgtddvst6mpb7p7ny</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200320204127/https://staff.fnwi.uva.nl/c.u.grelck/publications/BernGrelJessPPL10.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b3/9c/b39cc3a6d1587f7b5e37c68c4cbe02f68f0421a8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0129626410000053"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> worldscientific.com </button> </a>

Experimental Study of Energy-Minimizing Point Configurations on Spheres

Brandon Ballinger, Grigoriy Blekherman, Henry Cohn, Noah Giansiracusa, Elizabeth Kelly, Achill Schürmann
<span title="">2009</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6b4bprap7zebzpk5rd2nocdave" style="color: black;">Experimental Mathematics</a> </i> &nbsp;
We present experimental evidence for two new universal optima (consisting of 40 points in 10 dimensions and 64 points in 14 dimensions), as well as evidence that there are no others with at most 64 points  ...  We also describe several other new polytopes, and we present new geometrical descriptions of some of the known universal optima.  ...  For example, for five points in R 3 , the family with a square opposite a point does not contain a local minimum for harmonic energy.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/10586458.2009.10129052">doi:10.1080/10586458.2009.10129052</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fmnjfqd6abaorg5omgcuwcaqbi">fatcat:fmnjfqd6abaorg5omgcuwcaqbi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190222131739/http://pdfs.semanticscholar.org/38eb/083c0485b4ae5e114517ed7d679a07cab40e.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/38/eb/38eb083c0485b4ae5e114517ed7d679a07cab40e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/10586458.2009.10129052"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> tandfonline.com </button> </a>

Locally recoverable codes from planar graphs

Kathryn Haymaker, Justin O'Pella
<span title="2019-11-17">2019</span> <i title="Journal of Algebra Combinatorics Discrete Structures and Applications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3qhgdoxfkrcgrggfj5g24c3zpy" style="color: black;">Journal of Algebra Combinatorics Discrete Structures and Applications</a> </i> &nbsp;
The resulting edge codes are locally recoverable with availability two.  ...  We prove that the minimum distance of planar graph LRCs is equal to the girth of the graph, and we also establish a new bound on the rate of planar graph edge codes.  ...  The pre-print [5] is an extended version of the conference paper [4] and also contains results on the rate of optimal binary LRCs with small availability and locality.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.13069/jacodesmath.645021">doi:10.13069/jacodesmath.645021</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/j6k42ueqtngn3pxujok2lcmwxu">fatcat:j6k42ueqtngn3pxujok2lcmwxu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200216113522/https://dergipark.org.tr/tr/download/article-file/852066" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c0/13/c0131628171778b4afd5ec86b3272f9b2289d4ac.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.13069/jacodesmath.645021"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

A construction of optimal locally recoverable codes [article]

Xiaoru Li, Ziling Heng
<span title="2022-04-26">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The objective of this paper is to present a construction of near MDS codes with oval polynomials and then determine the locality of the codes.  ...  It turns out that the near MDS codes and their duals are both distance-optimal and dimension-optimal locally recoverable codes.  ...  In [12] , a class of optimal locally repairable codes of distances 3 and 4 with unbounded length was constructed.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2204.12034v1">arXiv:2204.12034v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s4urzm5elrfszjx46prf3ixule">fatcat:s4urzm5elrfszjx46prf3ixule</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220428151636/https://arxiv.org/pdf/2204.12034v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a7/1e/a71e086ef46b128a9ba0c837a9c40385c74e2f15.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2204.12034v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>
&laquo; Previous Showing results 1 &mdash; 15 out of 329,348 results