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Pairs of codes with prescribed Hamming distances and coincidences

Vince Grolmusz
<span title="">2006</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c45m6ttnaje4xbjsq7m2c6df2a" style="color: black;">Designs, Codes and Cryptography</a> </i> &nbsp;
In this work we describe a fast algorithm for generating pairs of q-ary codes with prescribed pairwise Hamming-distances and coincidences (for a letter s 2 f0; 1; : : : ; q ?  ...  The main problem of coding theory is to construct codes with large Hamming-distances between the code-words.  ...  The author also acknowledges the partial support of J anos Bolyai Fellowship, and research grants EU IST FET No. IST-2001-32012 and OTKA T030059.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10623-006-0016-4">doi:10.1007/s10623-006-0016-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yehjxqhg5ja3nd4ueng2h3uiru">fatcat:yehjxqhg5ja3nd4ueng2h3uiru</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190304085401/http://pdfs.semanticscholar.org/bae4/b1ee96752fb4f975f19ccda43d09da1a0c96.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/ba/e4/bae4b1ee96752fb4f975f19ccda43d09da1a0c96.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10623-006-0016-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

The chromatic number of the square of the $8$-cube

Janne I. Kokkala, Patric R. J. Östergård
<span title="2017-12-22">2017</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5bz4zmidbngqxk6yv4msbkm54u" style="color: black;">Mathematics of Computation</a> </i> &nbsp;
Consequently, a proper coloring of Q k n corresponds to a partition of the n-dimensional binary Hamming space into codes with minimum distance at least k + 1.  ...  This coloring problem can be considered in the framework of coding theory, as the graph Q k n can be constructed with one vertex for each binary word of length n and edges between vertices exactly when  ...  result to a pair of codewords in C i that would have distance less than 4) and consider the graph over the remaining codewords that has an edge between each pair of codewords with Hamming distance at  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/mcom/3291">doi:10.1090/mcom/3291</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6afwfvzw2vdmfn2ovdcpvilzta">fatcat:6afwfvzw2vdmfn2ovdcpvilzta</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190218172218/http://pdfs.semanticscholar.org/0e44/23481bede293b90f0d5afe14d4b0b8ddafdc.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/0e/44/0e4423481bede293b90f0d5afe14d4b0b8ddafdc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/mcom/3291"> <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>

The chromatic number of the square of the 8-cube [article]

Janne I. Kokkala, Patric R. J. Östergård
<span title="2016-07-06">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Consequently, a proper coloring of Q_n^k corresponds to a partition of the n-dimensional binary Hamming space into codes with minimum distance at least k+1.  ...  This coloring problem can be considered in the framework of coding theory, as the graph Q_n^k can be constructed with one vertex for each binary word of length n and edges between vertices exactly when  ...  result to a pair of codewords in C i that would have distance less than 4) and consider the graph over the remaining codewords that has an edge between each pair of codewords with Hamming distance at  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1607.01605v1">arXiv:1607.01605v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6qbi6as54rav5nbbaecdbp6p3u">fatcat:6qbi6as54rav5nbbaecdbp6p3u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191025000755/https://arxiv.org/pdf/1607.01605v1.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/c5/93/c593d1a953e16cfc19d6a9d8a06c32ce79c34b08.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1607.01605v1" 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>

Ternary Constant Weight Codes

Patric R. J. Östergård, Mattias Svanström
<span title="2002-10-15">2002</span> <i title="The Electronic Journal of Combinatorics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v5dyak6ulffqfara7hmuchh24a" style="color: black;">Electronic Journal of Combinatorics</a> </i> &nbsp;
Let $A_3(n,d,w)$ denote the maximum cardinality of a ternary code with length $n$, minimum distance $d$, and constant Hamming weight $w$.  ...  Methods for proving upper and lower bounds on $A_3(n,d,w)$ are presented, and a table of exact values and bounds in the range $n \leq 10$ is given.  ...  In this paper, we study ternary codes with given Hamming weight, and let A q (n, d, w) denote the maximum size of a q-ary code of length n, minimum distance d, and constant Hamming weight w (where the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.37236/1657">doi:10.37236/1657</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wmombqej35cpxi4vfdtw3it23a">fatcat:wmombqej35cpxi4vfdtw3it23a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706102554/http://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r41/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/15/8c/158c6f4586abe4caebfcf4d2aaeef1bf2c3b4440.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.37236/1657"> <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>

Short Barcodes for Next Generation Sequencing

Katharina Mir, Klaus Neuhaus, Martin Bossert, Steffen Schober, Eshel Ben-Jacob
<span title="2013-12-30">2013</span> <i title="Public Library of Science (PLoS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/s3gm7274mfe6fcs7e3jterqlri" style="color: black;">PLoS ONE</a> </i> &nbsp;
We provide a list of codes for lengths between six and eight nucleotides, where for length eight, two substitution errors can be corrected. In fact, no code with larger minimum distance can exist.  ...  The evaluation done is with respect to the error correction capabilities, barcode size and their experimental parameters and fundamental bounds on the code size and their distance properties.  ...  Senger, and A. Zeh for stimulating discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1371/journal.pone.0082933">doi:10.1371/journal.pone.0082933</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/24386128">pmid:24386128</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC3875435/">pmcid:PMC3875435</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5ui4oyk26zgmxncvpgddfdcmua">fatcat:5ui4oyk26zgmxncvpgddfdcmua</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171009115119/http://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0082933&amp;type=printable" 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/4b/03/4b03a773e7c196ef2b85c6c2cec84f0dd0a85fff.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1371/journal.pone.0082933"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> plos.org </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3875435" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

A new family of one-coincidence sets of sequences with dispersed elements for frequency hopping CDMA systems [article]

Lenny Fukshansky, Ahmad Adib Shaar
<span title="2017-12-08">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present a new family of one-coincidence sequence sets suitable for frequency hopping code division multiple access (FH-CDMA) systems with dispersed (low density) sequence elements.  ...  These sets are derived from one-coincidence prime sequence sets, such that for each one-coincidence prime sequence set there is a new one-coincidence set comprised of sequences with dispersed sequence  ...  Thus one can ask how big can a one-coincidence set of sequences of prescribed length and d req be? Lemma 3. 1 . 1 The elements of a sequence H k are all distinct.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1701.05209v2">arXiv:1701.05209v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ilnhzxzj7fh3jlqvroq2tvhxwe">fatcat:ilnhzxzj7fh3jlqvroq2tvhxwe</a> </span>
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Evolution of the genetic code through progressive symmetry breaking

Reijer Lenstra
<span title="">2014</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fydada535zbx7el5lxtbdrx6ga" style="color: black;">Journal of Theoretical Biology</a> </i> &nbsp;
This group preserves the differences between codons, known as Hamming distances, with a 1-distance corresponding to a single point mutation.  ...  The evolving codes transmit at most one message per codon block and as the number of messages increases so does the specificity of the code and of protein synthesis.  ...  Hamming distances and the CodonGraph The InterCodon Distance Matrix of Supplemental material 1 shows the Hamming distances between the 64 codons (Section 2) as a 64 Â 64 matrix with the codons indexing  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jtbi.2014.01.002">doi:10.1016/j.jtbi.2014.01.002</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/24434741">pmid:24434741</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6wm3wjpvg5dvlguahncrbwg6cy">fatcat:6wm3wjpvg5dvlguahncrbwg6cy</a> </span>
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Bounds on the dimension of codes and subcodes with prescribed contraction index

Alexander Vardy, Jakov Snyders, Yair Be'ery
<span title="">1990</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wsx3rzhpingfvewcn5nwhfkq3e" style="color: black;">Linear Algebra and its Applications</a> </i> &nbsp;
We also present an upper bound on the dimension of any linear code over GF(9) of length n, minimum Hamming distance d, and contraction index A.  ...  We derive several upper and lower bounds on the dimension of a proper subcode of 4 with a prescribed contraction index v < A.  ...  In the sequel d L denotes the minimum Hamming distance of (8*)' THEOREM 8. For any pair of integers u and p such that 0 < v < p <h-l, J(v) <n*- Proof. Consider the case v = CL.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0024-3795(90)90269-i">doi:10.1016/0024-3795(90)90269-i</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xmowppho25azbiodnxvv24zk4e">fatcat:xmowppho25azbiodnxvv24zk4e</a> </span>
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On Coset Leader Graphs of LDPC Codes

Eran Iceland, Alex Samorodnitsky
<span title="">2015</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/niovmjummbcwdg4qshgzykkpfu" style="color: black;">IEEE Transactions on Information Theory</a> </i> &nbsp;
This improvement, combined with the techniques of [2], improves the rate vs distance bounds for LDPC codes in a significant sub-range of relative distances.  ...  Following the approach of [1], we use this fact to improve on the first linear programming bound on the rate of LDPC codes, as the function of their minimal relative distance.  ...  Acknowledgment We would like to thank the anonymous referees for their numerous suggestions that led to a significant improvement in the presentation of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tit.2015.2438716">doi:10.1109/tit.2015.2438716</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s5rolqpbpfgchhwqv3ykm6ahq4">fatcat:s5rolqpbpfgchhwqv3ykm6ahq4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20151216173156/http://www.cs.huji.ac.il/~salex/papers/coset_leader_graphs.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/43/c2/43c26b44dd9cb0c23447be891a35fa8fe1435681.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tit.2015.2438716"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

One more proof of the first linear programming bound for binary codes and two conjectures [article]

Alex Samorodnitsky
<span title="2021-04-29">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A binary code with minimal distance δ n is small because the projections of the characteristic functions of its elements on the subspace spanned by the Walsh-Fourier characters of weight up to (1/2 - √  ...  The conjecture for linear codes is related to and is influenced by conjectures of Håstad and of Kalai and Linial.  ...  We pass to the proof of Lemma 4.3. Proof: (Lemma 4.3) Acknowledgement We are grateful to Johan Håstad for his permission to publish his conjecture (see (1)) in our paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2104.14587v1">arXiv:2104.14587v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/knjj7lwot5b4nc2ftmnu4xorm4">fatcat:knjj7lwot5b4nc2ftmnu4xorm4</a> </span>
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On Coset Leader Graphs of LDPC Codes [article]

Eran Iceland, Alex Samorodnitsky
<span title="2014-12-16">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This improvement, combined with the techniques of Ben-Haim and Lytsin (2006), improves the rate vs distance bounds for LDPC codes in a significant sub-range of relative distances.  ...  Following the approach of Friedman and Tillich (2006), we use this fact to improve on the first linear programming bound on the rate of LDPC codes, as the function of their minimal distance.  ...  Acknowledgment We would like to thank the anonymous referees for their numerous suggestions that led to a significant improvement in the presentation of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1402.5051v2">arXiv:1402.5051v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ue5sndhu5bcltf4if5plys3a7e">fatcat:ue5sndhu5bcltf4if5plys3a7e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191016162043/https://arxiv.org/pdf/1402.5051v2.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/49/72/4972bbe2589862cf71150e9ba8da998b4a9266b4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1402.5051v2" 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>

Sum-Rank BCH Codes and Cyclic-Skew-Cyclic Codes [article]

Umberto Martínez-Peñas
<span title="2021-06-08">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Sum-rank BCH codes, with prescribed minimum sum-rank distance, are then defined as the largest cyclic-skew-cyclic codes whose defining set contains such consecutive pairs.  ...  Finally, a decoder for sum-rank BCH codes up to half their prescribed distance is obtained.  ...  It is left to the reader to show that (41) may be equal to the Singleton bound (4) for the prescribed distance δ if, and only if, s = 1, which is the case in which SR-BCH codes coincide with CSC linearized  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2009.04949v2">arXiv:2009.04949v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/snby3dj6azclxgu4kyacklli44">fatcat:snby3dj6azclxgu4kyacklli44</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210615132609/https://arxiv.org/pdf/2009.04949v2.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/5a/ce/5ace772228873c6adcedd54e1b503aaa35dd5a0a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2009.04949v2" 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>

A new family of one-coincidence sets of sequences with dispersed elements for frequency hopping cdma systems

Lenny Fukshansky, Ahmad A. Shaar
<span title="">2018</span> <i title="American Institute of Mathematical Sciences (AIMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jbbcig2iqnbuvngg7spzuoozwu" style="color: black;">Advances in Mathematics of Communications</a> </i> &nbsp;
We present a new family of one-coincidence sequence sets suitable for frequency hopping code division multiple access (FH-CDMA) systems with dispersed (low density) sequence elements.  ...  These sets are derived from one-coincidence prime sequence sets, such that for each one-coincidence prime sequence set there is a new one-coincidence set comprised of sequences with dispersed sequence  ...  Mahesh Kotecha, and Mrs. Mitzi Perdue: for their support he is very grateful. He also acknowledges useful discussions with Prof. R. Olson and Prof. A. Aswad.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3934/amc.2018012">doi:10.3934/amc.2018012</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2pl5i2biuvhmpmv6qggjg72rki">fatcat:2pl5i2biuvhmpmv6qggjg72rki</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190216030155/http://pdfs.semanticscholar.org/005f/b4341738c9ddc8d4c2db0c5301f3027b7774.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/00/5f/005fb4341738c9ddc8d4c2db0c5301f3027b7774.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3934/amc.2018012"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

When data must satisfy constraints upon writing

Erik Ordentlich, Ron M. Roth
<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;
We shall refer to a set of constrained sequences with this property as being Hamming connected.  ...  We shall refer to a set of constrained sequences with this property as being Hamming connected.  ...  the Hamming distance between the sequences x and y.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isit.2014.6875235">doi:10.1109/isit.2014.6875235</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/isit/OrdentlichR14.html">dblp:conf/isit/OrdentlichR14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jbr6vvbotrbsxka4zigzi4eapu">fatcat:jbr6vvbotrbsxka4zigzi4eapu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808164734/http://www.hpl.hp.com/techreports/2014/HPL-2014-19.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/66/04/6604032d3edfaf7f63f275723096712e8519ef65.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isit.2014.6875235"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Generalized Hamming weights of nonlinear codes and the relation to the Z/sub 4/-linear representation

I. Reuven, Y. Be'ery
<span title="">1999</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/niovmjummbcwdg4qshgzykkpfu" style="color: black;">IEEE Transactions on Information Theory</a> </i> &nbsp;
In this correspondence, we give a new definition of generalized Hamming weights of nonlinear codes and a new interpretation connected with it.  ...  The new definition is invariant under translates of the code, it satisfies the property of strict monotonicity and the generalized Singleton bound.  ...  Cohen for directing them to [3] and [7] . The discussions with him while the second author visited ENST, Paris, were the origin of the new definition of the GHW. The authors also wish to thank Y.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/18.749020">doi:10.1109/18.749020</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c6ots4qjznarxh3et2cdhuwvmq">fatcat:c6ots4qjznarxh3et2cdhuwvmq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20140910194355/http://www.eng.tau.ac.il/~ybeery/papers/1999-3-reuven-b.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/48/48/48481e96cdfb2fa315a58ec320d5f1edb19cc38c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/18.749020"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>
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