New bounds on a hypercube coloring problem and linear codes

In studying the scalability of optical networks, one problem arising involves coloring the vertices of the n-dimensional hypercube with as few colors as possible such that any two vertices whose Hamming distance is at most k are colored differently. Determining the exact value of /spl chi//sub k~/(n...

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1. Verfasser:	Hung Quang Ngo
Format:	Tagungsbericht
Sprache:	eng
Schlagworte:	Block codes Computer science Hamming distance Hypercubes Linear code Optical fiber networks Scalability Sun Upper bound Vectors
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creator	Hung Quang Ngo
description	In studying the scalability of optical networks, one problem arising involves coloring the vertices of the n-dimensional hypercube with as few colors as possible such that any two vertices whose Hamming distance is at most k are colored differently. Determining the exact value of /spl chi//sub k~/(n), the minimum number of colors needed, appears to be a difficult problem. We improve the known lower and upper bounds of /spl chi//sub k~/(n) and indicate the connection of this colouring problem to linear codes.
doi_str_mv	10.1109/ITCC.2001.918853
format	Conference Proceeding
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Determining the exact value of /spl chi//sub k~/(n), the minimum number of colors needed, appears to be a difficult problem. We improve the known lower and upper bounds of /spl chi//sub k~/(n) and indicate the connection of this colouring problem to linear codes.</description><identifier>ISBN: 9780769510620</identifier><identifier>ISBN: 0769510620</identifier><identifier>DOI: 10.1109/ITCC.2001.918853</identifier><language>eng</language><publisher>IEEE</publisher><subject>Block codes ; Computer science ; Hamming distance ; Hypercubes ; Linear code ; Optical fiber networks ; Scalability ; Sun ; Upper bound ; Vectors</subject><ispartof>Proceedings International Conference on Information Technology: Coding and Computing, 2001, p.542-546</ispartof><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/918853$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>309,310,776,780,785,786,2052,4036,4037,27902,54895</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/918853$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Hung Quang Ngo</creatorcontrib><title>New bounds on a hypercube coloring problem and linear codes</title><title>Proceedings International Conference on Information Technology: Coding and Computing</title><addtitle>ITCC</addtitle><description>In studying the scalability of optical networks, one problem arising involves coloring the vertices of the n-dimensional hypercube with as few colors as possible such that any two vertices whose Hamming distance is at most k are colored differently. Determining the exact value of /spl chi//sub k~/(n), the minimum number of colors needed, appears to be a difficult problem. We improve the known lower and upper bounds of /spl chi//sub k~/(n) and indicate the connection of this colouring problem to linear codes.</description><subject>Block codes</subject><subject>Computer science</subject><subject>Hamming distance</subject><subject>Hypercubes</subject><subject>Linear code</subject><subject>Optical fiber networks</subject><subject>Scalability</subject><subject>Sun</subject><subject>Upper bound</subject><subject>Vectors</subject><isbn>9780769510620</isbn><isbn>0769510620</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2001</creationdate><recordtype>conference_proceeding</recordtype><sourceid>6IE</sourceid><sourceid>RIE</sourceid><recordid>eNotj0tLxDAURgMiKGP34ip_oPWmefQGV1J8DAy6GddDmtxopNOWxEHm3zswfpuzOHDgY-xWQCME2Pv1tu-bFkA0ViBqecEq2yF0xmoBpoUrVpXyDacpraTR1-zhjX75MB-mUPg8cce_jgtlfxiI-3mcc5o--ZLnYaQ9d1PgY5rI5ZMLVG7YZXRjoeqfK_bx_LTtX-vN-8u6f9zUSXTqp44Y0apgvFMotNEKvUQVowRN2igE50P0SnQ-SCm1dmBbN9CA0hhCG-SK3Z27iYh2S057l4-780P5Bx2vRZY</recordid><startdate>2001</startdate><enddate>2001</enddate><creator>Hung Quang Ngo</creator><general>IEEE</general><scope>6IE</scope><scope>6IL</scope><scope>CBEJK</scope><scope>RIE</scope><scope>RIL</scope></search><sort><creationdate>2001</creationdate><title>New bounds on a hypercube coloring problem and linear codes</title><author>Hung Quang Ngo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-i174t-f8f894d6ca48156548c384ff305e56480acdfc417cd33355a092abeb8366e89d3</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Block codes</topic><topic>Computer science</topic><topic>Hamming distance</topic><topic>Hypercubes</topic><topic>Linear code</topic><topic>Optical fiber networks</topic><topic>Scalability</topic><topic>Sun</topic><topic>Upper bound</topic><topic>Vectors</topic><toplevel>online_resources</toplevel><creatorcontrib>Hung Quang Ngo</creatorcontrib><collection>IEEE Electronic Library (IEL) Conference Proceedings</collection><collection>IEEE Proceedings Order Plan All Online (POP All Online) 1998-present by volume</collection><collection>IEEE Xplore All Conference Proceedings</collection><collection>IEEE Electronic Library (IEL)</collection><collection>IEEE Proceedings Order Plans (POP All) 1998-Present</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Hung Quang Ngo</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>New bounds on a hypercube coloring problem and linear codes</atitle><btitle>Proceedings International Conference on Information Technology: Coding and Computing</btitle><stitle>ITCC</stitle><date>2001</date><risdate>2001</risdate><spage>542</spage><epage>546</epage><pages>542-546</pages><isbn>9780769510620</isbn><isbn>0769510620</isbn><abstract>In studying the scalability of optical networks, one problem arising involves coloring the vertices of the n-dimensional hypercube with as few colors as possible such that any two vertices whose Hamming distance is at most k are colored differently. Determining the exact value of /spl chi//sub k~/(n), the minimum number of colors needed, appears to be a difficult problem. We improve the known lower and upper bounds of /spl chi//sub k~/(n) and indicate the connection of this colouring problem to linear codes.</abstract><pub>IEEE</pub><doi>10.1109/ITCC.2001.918853</doi><tpages>5</tpages></addata></record>
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identifier	ISBN: 9780769510620
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subjects	Block codes Computer science Hamming distance Hypercubes Linear code Optical fiber networks Scalability Sun Upper bound Vectors
title	New bounds on a hypercube coloring problem and linear codes
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