Solving Linear Equations Parameterized by Hamming Weight

Given a system of linear equations A x = b over the binary field F 2 and an integer t ≥ 1 , we study the following three algorithmic problems: Does A x = b have a solution of weight at most t ? Does A x = b have a solution of weight exactly t ? Does A x = b have a solution of weight at least t ? We...

Full description

Saved in:

Bibliographic Details
Published in:	Algorithmica Vol. 75; no. 2; pp. 322 - 338
Main Authors:	Arvind, V., Köbler, Johannes, Kuhnert, Sebastian, Torán, Jacobo
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.06.2016
Subjects:	Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Theory of Computation Graph Match Problem Brute Force Search Deterministic Polynomial Time Internal Vertex Logarithmic Space
ISSN:	0178-4617, 1432-0541
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	Given a system of linear equations A x = b over the binary field F 2 and an integer t ≥ 1 , we study the following three algorithmic problems: Does A x = b have a solution of weight at most t ? Does A x = b have a solution of weight exactly t ? Does A x = b have a solution of weight at least t ? We investigate the parameterized complexity of these problems with t as parameter. A special aspect of our study is to show how the maximum multiplicity k of variable occurrences in A x = b influences the complexity of the problem. We show a sharp dichotomy: for each k ≥ 3 the first two problems are W [ 1 ] -hard [which strengthens and simplifies a result of Downey et al. (SIAM J Comput 29(2), 545–570, 1999 )]. For k = 2 , the problems turn out to be intimately connected to well-studied matching problems and can be efficiently solved using matching algorithms.
AbstractList	Given a system of linear equations A x = b over the binary field F 2 and an integer t ≥ 1 , we study the following three algorithmic problems: Does A x = b have a solution of weight at most t ? Does A x = b have a solution of weight exactly t ? Does A x = b have a solution of weight at least t ? We investigate the parameterized complexity of these problems with t as parameter. A special aspect of our study is to show how the maximum multiplicity k of variable occurrences in A x = b influences the complexity of the problem. We show a sharp dichotomy: for each k ≥ 3 the first two problems are W [ 1 ] -hard [which strengthens and simplifies a result of Downey et al. (SIAM J Comput 29(2), 545–570, 1999 )]. For k = 2 , the problems turn out to be intimately connected to well-studied matching problems and can be efficiently solved using matching algorithms.
Author	Kuhnert, Sebastian Köbler, Johannes Arvind, V. Torán, Jacobo
Author_xml	– sequence: 1 givenname: V. surname: Arvind fullname: Arvind, V. organization: Institute of Mathematical Sciences – sequence: 2 givenname: Johannes surname: Köbler fullname: Köbler, Johannes organization: Institut für Informatik, Humboldt-Universität zu Berlin – sequence: 3 givenname: Sebastian orcidid: 0000-0003-2197-5803 surname: Kuhnert fullname: Kuhnert, Sebastian email: kuhnert@informatik.hu-berlin.de organization: Institut für Informatik, Humboldt-Universität zu Berlin – sequence: 4 givenname: Jacobo surname: Torán fullname: Torán, Jacobo organization: Institut für Theoretische Informatik, Universität Ulm
BookMark	eNp9j81KAzEYRYNUsK0-gLt5geiXZDLJLKVUWygoWHAZMvmpKZ2MJlOhPr1T68pFV3dzz-WeCRrFLjqEbgncEQBxnwFKzjAQjgFqidkFGpOSUQy8JCM0BiIkLisirtAk5y0AoaKuxki-druvEDfFKkSnUzH_3Os-dDEXLzrp1vUuhW9ni-ZQLHTbHptvLmze-2t06fUuu5u_nKL143w9W-DV89Ny9rDChvGyx41prKEcXOM9o0IzV2kGTgjLBBivZVNzI6StKs-Aakm1pVaLpvTSUl6zKRKnWZO6nJPzyoT-92GfdNgpAuror07-avBXR3_FBpL8Iz9SaHU6nGXoiclDN25cUttun-Lgdwb6ARY_b6s
CitedBy_id	crossref_primary_10_1007_s00453_021_00867_y crossref_primary_10_1155_2022_3411959 crossref_primary_10_1007_s00453_016_0229_5
Cites_doi	10.1145/322307.322309 10.1109/TIT.1978.1055873 10.1109/TIT.1981.1056419 10.1007/BF02579206 10.1109/TIT.2012.2209198 10.1145/210332.210337 10.1016/j.jcss.2009.04.001 10.1007/978-1-4471-5559-1 10.1109/18.641542 10.1007/BF01683259 10.1145/1077464.1077476 10.1007/s00037-005-0195-9 10.1007/BF01293484 10.1137/S0097539797323571 10.1007/978-1-4612-0515-9 10.1145/258533.258559 10.1145/1391289.1391291 10.1109/FOCS.2010.21
ContentType	Journal Article
Copyright	Springer Science+Business Media New York 2015
Copyright_xml	– notice: Springer Science+Business Media New York 2015
DBID	AAYXX CITATION
DOI	10.1007/s00453-015-0098-3
DatabaseName	CrossRef
DatabaseTitle	CrossRef
DatabaseTitleList
DeliveryMethod	fulltext_linktorsrc
Discipline	Computer Science
EISSN	1432-0541
EndPage	338
ExternalDocumentID	10_1007_s00453_015_0098_3
GrantInformation_xml	– fundername: Deutsche Forschungsgemeinschaft grantid: KO 1053/7-2 funderid: http://dx.doi.org/10.13039/501100001659 – fundername: Alexander von Humboldt-Stiftung grantid: DEU/1115695 funderid: http://dx.doi.org/10.13039/100005156
GroupedDBID	-4Z -59 -5G -BR -EM -Y2 -~C -~X .86 .DC .VR 06D 0R~ 0VY 199 1N0 1SB 203 23M 28- 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAOBN AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDPE ABDZT ABECU ABFSI ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTAH ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BBWZM BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP E.L EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAS LLZTM M4Y MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P9O PF- PT4 PT5 QOK QOS R4E R89 R9I RHV RIG RNI RNS ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCJ SCLPG SCO SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TN5 TSG TSK TSV TUC U2A UG4 UOJIU UQL UTJUX UZXMN VC2 VFIZW VH1 VXZ W23 W48 WK8 YLTOR Z45 Z7X Z83 Z88 Z8R Z8W Z92 ZMTXR ZY4 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION
ID	FETCH-LOGICAL-c354t-bcbdc250ebff327a3e6a30e77d370cfa8b95c78d66f302a82ad2da7b4f8d2593
IEDL.DBID	RSV
ISICitedReferencesCount	9
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000376981100006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0178-4617
IngestDate	Sat Nov 29 02:20:27 EST 2025 Tue Nov 18 22:20:54 EST 2025 Fri Feb 21 02:40:22 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	2
Keywords	Graph Match Problem Brute Force Search Deterministic Polynomial Time Internal Vertex Logarithmic Space
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c354t-bcbdc250ebff327a3e6a30e77d370cfa8b95c78d66f302a82ad2da7b4f8d2593
ORCID	0000-0003-2197-5803
PageCount	17
ParticipantIDs	crossref_citationtrail_10_1007_s00453_015_0098_3 crossref_primary_10_1007_s00453_015_0098_3 springer_journals_10_1007_s00453_015_0098_3
PublicationCentury	2000
PublicationDate	2016-06-01
PublicationDateYYYYMMDD	2016-06-01
PublicationDate_xml	– month: 06 year: 2016 text: 2016-06-01 day: 01
PublicationDecade	2010
PublicationPlace	New York
PublicationPlace_xml	– name: New York
PublicationTitle	Algorithmica
PublicationTitleAbbrev	Algorithmica
PublicationYear	2016
Publisher	Springer US
Publisher_xml	– name: Springer US
References	Marx (CR14) 2005; 14 Bodlaender, Downey, Fellows, Hermelin (CR2) 2009; 75 Vardy (CR18) 1997; 43 Mulmuley, Vazirani, Vazirani (CR15) 1987; 7 CR19 CR17 Berlekamp, McEliece, van Tilborg (CR4) 1978; 24 Cheng, Wan (CR6) 2012; 58 Bruschi, Ravasio (CR5) 1995; 13 CR10 Alon, Yuster, Zwick (CR1) 1995; 42 Buntrock, Damm, Hertrampf, Meinel (CR3) 1992; 25 Jones, Edmund Lien, Laaser (CR11) 1976; 10 Ntafos, Louis Hakimi (CR13) 1981; 27 Downey, Fellows, Vardy, Whittle (CR9) 1999; 29 Johnson (CR12) 2005; 1 Papadimitriou, Yannakakis (CR16) 1982; 29 Downey, Fellows (CR8) 2013 Downey, Fellows (CR7) 1999 A Vardy (98_CR18) 1997; 43 98_CR10 D Marx (98_CR14) 2005; 14 HL Bodlaender (98_CR2) 2009; 75 D Bruschi (98_CR5) 1995; 13 SC Ntafos (98_CR13) 1981; 27 G Buntrock (98_CR3) 1992; 25 C Papadimitriou (98_CR16) 1982; 29 ND Jones (98_CR11) 1976; 10 DS Johnson (98_CR12) 2005; 1 K Mulmuley (98_CR15) 1987; 7 N Alon (98_CR1) 1995; 42 RG Downey (98_CR8) 2013 RG Downey (98_CR9) 1999; 29 RG Downey (98_CR7) 1999 Q Cheng (98_CR6) 2012; 58 98_CR17 98_CR19 ER Berlekamp (98_CR4) 1978; 24
References_xml	– volume: 29 start-page: 285 year: 1982 end-page: 309 ident: CR16 article-title: The complexity of restricted spanning tree problems publication-title: J. ACM doi: 10.1145/322307.322309 – ident: CR19 – volume: 24 start-page: 384 year: 1978 end-page: 386 ident: CR4 article-title: On the inherent intractability of certain coding problems publication-title: IEEE Trans. Inform. Theory doi: 10.1109/TIT.1978.1055873 – volume: 27 start-page: 794 issue: 6 year: 1981 end-page: 796 ident: CR13 article-title: On the complexity of some coding problems publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.1981.1056419 – volume: 7 start-page: 105 year: 1987 end-page: 113 ident: CR15 article-title: Matching is as easy as matrix inversion publication-title: Combinatorica doi: 10.1007/BF02579206 – volume: 25 start-page: 223 issue: 3 year: 1992 end-page: 237 ident: CR3 article-title: Structure and importance of logspace-MOD class publication-title: Theory Comput. Syst. – volume: 58 start-page: 6935 year: 2012 end-page: 6941 ident: CR6 article-title: A deterministic reduction for the gap minimum distance problem publication-title: IEEE Trans. Inform. Theory doi: 10.1109/TIT.2012.2209198 – volume: 42 start-page: 844 issue: 4 year: 1995 end-page: 856 ident: CR1 article-title: Color coding publication-title: J. ACM doi: 10.1145/210332.210337 – ident: CR17 – volume: 75 start-page: 423 issue: 8 year: 2009 end-page: 434 ident: CR2 article-title: On problems without polynomial kernels publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2009.04.001 – ident: CR10 – year: 2013 ident: CR8 publication-title: Fundamentals of Parameterized Complexity doi: 10.1007/978-1-4471-5559-1 – volume: 43 start-page: 1757 year: 1997 end-page: 1766 ident: CR18 article-title: The intractability of computing the minimum distance of a code publication-title: IEEE Trans. Inform. Theory doi: 10.1109/18.641542 – volume: 10 start-page: 1 issue: 1 year: 1976 end-page: 17 ident: CR11 article-title: New problems complete for nondeterministic log space publication-title: Math. Syst. Theory doi: 10.1007/BF01683259 – volume: 1 start-page: 160 issue: 1 year: 2005 end-page: 176 ident: CR12 article-title: The NP-completeness column publication-title: ACM Trans. Algorithms doi: 10.1145/1077464.1077476 – volume: 14 start-page: 153 issue: 2 year: 2005 end-page: 183 ident: CR14 article-title: Parameterized complexity of constraint satisfaction problems publication-title: Comput. Complex. doi: 10.1007/s00037-005-0195-9 – volume: 13 start-page: 346 issue: 4 year: 1995 end-page: 356 ident: CR5 article-title: Random parallel algorithms for finding exact branchings, perfect matchings, and cycles publication-title: Algorithmica doi: 10.1007/BF01293484 – volume: 29 start-page: 545 issue: 2 year: 1999 end-page: 570 ident: CR9 article-title: The parametrized complexity of some fundamental problems in coding theory publication-title: SIAM J. Comput. doi: 10.1137/S0097539797323571 – year: 1999 ident: CR7 publication-title: Parameterized Complexity doi: 10.1007/978-1-4612-0515-9 – volume: 75 start-page: 423 issue: 8 year: 2009 ident: 98_CR2 publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2009.04.001 – volume-title: Fundamentals of Parameterized Complexity year: 2013 ident: 98_CR8 doi: 10.1007/978-1-4471-5559-1 – volume: 43 start-page: 1757 year: 1997 ident: 98_CR18 publication-title: IEEE Trans. Inform. Theory doi: 10.1109/18.641542 – volume: 25 start-page: 223 issue: 3 year: 1992 ident: 98_CR3 publication-title: Theory Comput. Syst. – volume: 10 start-page: 1 issue: 1 year: 1976 ident: 98_CR11 publication-title: Math. Syst. Theory doi: 10.1007/BF01683259 – ident: 98_CR19 doi: 10.1145/258533.258559 – volume: 24 start-page: 384 year: 1978 ident: 98_CR4 publication-title: IEEE Trans. Inform. Theory doi: 10.1109/TIT.1978.1055873 – volume: 27 start-page: 794 issue: 6 year: 1981 ident: 98_CR13 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.1981.1056419 – volume: 13 start-page: 346 issue: 4 year: 1995 ident: 98_CR5 publication-title: Algorithmica doi: 10.1007/BF01293484 – volume: 29 start-page: 285 year: 1982 ident: 98_CR16 publication-title: J. ACM doi: 10.1145/322307.322309 – volume: 7 start-page: 105 year: 1987 ident: 98_CR15 publication-title: Combinatorica doi: 10.1007/BF02579206 – ident: 98_CR17 doi: 10.1145/1391289.1391291 – volume: 1 start-page: 160 issue: 1 year: 2005 ident: 98_CR12 publication-title: ACM Trans. Algorithms doi: 10.1145/1077464.1077476 – volume: 14 start-page: 153 issue: 2 year: 2005 ident: 98_CR14 publication-title: Comput. Complex. doi: 10.1007/s00037-005-0195-9 – volume: 58 start-page: 6935 year: 2012 ident: 98_CR6 publication-title: IEEE Trans. Inform. Theory doi: 10.1109/TIT.2012.2209198 – volume: 29 start-page: 545 issue: 2 year: 1999 ident: 98_CR9 publication-title: SIAM J. Comput. doi: 10.1137/S0097539797323571 – ident: 98_CR10 doi: 10.1109/FOCS.2010.21 – volume: 42 start-page: 844 issue: 4 year: 1995 ident: 98_CR1 publication-title: J. ACM doi: 10.1145/210332.210337 – volume-title: Parameterized Complexity year: 1999 ident: 98_CR7 doi: 10.1007/978-1-4612-0515-9
SSID	ssj0012796
Score	2.1506894
Snippet	Given a system of linear equations A x = b over the binary field F 2 and an integer t ≥ 1 , we study the following three algorithmic problems: Does A x = b...
SourceID	crossref springer
SourceType	Enrichment Source Index Database Publisher
StartPage	322
SubjectTerms	Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Theory of Computation
Title	Solving Linear Equations Parameterized by Hamming Weight
URI	https://link.springer.com/article/10.1007/s00453-015-0098-3
Volume	75
WOSCitedRecordID	wos000376981100006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVAVX databaseName: Springer Nature - Connect here FIRST to enable access customDbUrl: eissn: 1432-0541 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0012796 issn: 0178-4617 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LSwMxEB60evBifWJ9kYMnZWG72U3So0iLp1Js0d6WJJOAUFrtVkF_vUn2AQUV9D77YJjJPPN9AFc6ZiZD5vxbCxOlzOVwKkMboYenk90MqbGBbIIPh2I67Y2qe9xFve1ejyTDSd1cdvPZh9_9yaIAgkk3YctFO-H5Gh7Gj83oIOGBlMvTzrtvd3k9yvzuFevBaH0SGgLMoP2vX9uD3SqfJLelAezDhpkfQLvmaiCV6x6CGC9mvndAXPHpjJv0X0uM74KMpN_P8pDNnwaJ-iC-me0ln0LX9Agmg_7k7j6qWBMiTbN0FSmtULvExihracIlNUzS2HCOlMfaSqF6meYCGbM0TqRIJCYouUqtQFcL0WNozRdzcwIkRYwzYV1Nk2KqlZXKCldf6ERKqruadSCutZfrClHcE1vM8gYLOSgmd4rJvWJy2oHr5pGXEk7jN-GbWt155VnFz9Knf5I-gx2X-rBy6escWqvlm7mAbf2-ei6Wl8GivgBRNcVj
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1JSwMxFH5oFfRiXbGuOXhSBqaTmSQ9irRUrKXYor0NWUEorXaqoL_eJLNAQQW9v1l4vJe35vsALmRIdKKI9W_JdBATm8OJRJlAOXg63kwU1saTTdB-n43HrUFxjzsrt93LkaQ_qavLbi77cLs_SeBBMPEqrMU2YDnA_IfhYzU6iKgn5XK08_bbTVqOMr97xXIwWp6E-gDTqf_r17Zhq8gn0XVuADuwoqe7UC-5GlDhunvAhrOJ6x0gW3xa40bt1xzjO0MD7vazHGTzp1ZIfCDXzHaST75rug-jTnt00w0K1oRA4iReBEIKJW1io4UxOKIca8JxqClVmIbScCZaiaRMEWJwGHEWcRUpTkVsmLK1ED6A2nQ21YeAYqXChBlb08QqlsJwYZitL2TEOZZNSRoQltpLZYEo7ogtJmmFhewVk1rFpE4xKW7AZfXISw6n8ZvwVanutPCs7Gfpoz9Jn8NGd3TfS3u3_btj2LRpEMkXwE6gtpi_6VNYl--L52x-5q3rC5wpyEc
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEB60inixPrE-9-BJCU2zye72KNqiKKXQor2FfYJQ0tpEQX-9u3lBQQXxPgnLMMN-89jvA7iQPtGRIja_JdNeSCyGE5EynnL0dLwTKaxNLjZBBwM2mXSHpc5pWm27VyPJ4k2DY2lKsvZcmXb98M0hEbcHFHk5ISZehbXQ7dG7cn30VI8RApoLdDkJenuODq3Gmt_9YvliWp6K5pdNv_nvY27DVokz0XURGDuwopNdaFYaDqhM6T1go9nU9RSQLUpt0KPea8H9naIhd3tbjsr5UyskPpBrcjvL57ybug_jfm98c-eVagqexFGYeUIKJS3g0cIYHFCONeHY15QqTH1pOBPdSFKmCDHYDzgLuAoUpyI0TNkaCR9AI5kl-hBQqJQfMWNrnVCFUhguDLN1hww4x7IjSQv8ypOxLJnGneDFNK45knPHxNYxsXNMjFtwWX8yL2g2fjO-qlwflxmX_mx99Cfrc9gY3vbjx_vBwzFsWnREir2wE2hkizd9CuvyPXtJF2d5oH0BgiDRKw
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Solving+Linear+Equations+Parameterized+by+Hamming+Weight&rft.jtitle=Algorithmica&rft.au=Arvind%2C+V.&rft.au=K%C3%B6bler%2C+Johannes&rft.au=Kuhnert%2C+Sebastian&rft.au=Tor%C3%A1n%2C+Jacobo&rft.date=2016-06-01&rft.issn=0178-4617&rft.eissn=1432-0541&rft.volume=75&rft.issue=2&rft.spage=322&rft.epage=338&rft_id=info:doi/10.1007%2Fs00453-015-0098-3&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s00453_015_0098_3
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0178-4617&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0178-4617&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0178-4617&client=summon