On covering problems of codes
Abstract LetC be a binary code of lengthn (i.e., a subset of {0, 1}n). TheCovering Radius of C is the smallest integerr such that each vector in {0, 1}n is at a distance at mostr from some code word. Our main result is that the decision problem associated with the Covering Radius of arbitrary binary...
Ausführliche Beschreibung
Autor*in: |
Frances, M. [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
1997 |
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Schlagwörter: |
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Anmerkung: |
© Springer-Verlag New York Inc 1997 |
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Übergeordnetes Werk: |
Enthalten in: Theory of computing systems - New York, NY : Springer, 1997, 30(1997), 2 vom: Apr., Seite 113-119 |
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Übergeordnetes Werk: |
volume:30 ; year:1997 ; number:2 ; month:04 ; pages:113-119 |
Links: |
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DOI / URN: |
10.1007/BF02679443 |
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Katalog-ID: |
SPR002489074 |
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041 | |a eng | ||
100 | 1 | |a Frances, M. |e verfasserin |4 aut | |
245 | 1 | 0 | |a On covering problems of codes |
264 | 1 | |c 1997 | |
336 | |a Text |b txt |2 rdacontent | ||
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500 | |a © Springer-Verlag New York Inc 1997 | ||
520 | |a Abstract LetC be a binary code of lengthn (i.e., a subset of {0, 1}n). TheCovering Radius of C is the smallest integerr such that each vector in {0, 1}n is at a distance at mostr from some code word. Our main result is that the decision problem associated with the Covering Radius of arbitrary binary codes is NP-complete. This result is established as follows. TheRadius of a binary codeC is the smallest integerr such thatC is contained in a radius-r ball of the Hamming metric space 〈{0, 1}n,d〉. It is known [K] that the problems of computing the Radius and the Covering Radius are equivalent. We show that the 3SAT problem is polynomially reducible to the Radius decision problem. A central tool in our reduction is a metrical characterization of the set ofdoubled vectors of length 2n: {v=(v1v2 …v2n) | ∀i:v2i=v2i−1}. We show that there is a setY ⊂ {0, 1}2n such that for everyv ε {0, 1}2n:v is doubled iffY is contained in the radius-n ball centered atv; moreover,Y can be constructed in time polynomial inn. | ||
650 | 4 | |a Linear Code |7 (dpeaa)DE-He213 | |
650 | 4 | |a Covering Problem |7 (dpeaa)DE-He213 | |
650 | 4 | |a Code Word |7 (dpeaa)DE-He213 | |
650 | 4 | |a Covering Radius |7 (dpeaa)DE-He213 | |
650 | 4 | |a Minimum Radius |7 (dpeaa)DE-He213 | |
700 | 1 | |a Litman, A. |4 aut | |
773 | 0 | 8 | |i Enthalten in |t Theory of computing systems |d New York, NY : Springer, 1997 |g 30(1997), 2 vom: Apr., Seite 113-119 |w (DE-627)254909728 |w (DE-600)1463181-7 |x 1433-0490 |7 nnns |
773 | 1 | 8 | |g volume:30 |g year:1997 |g number:2 |g month:04 |g pages:113-119 |
856 | 4 | 0 | |u https://dx.doi.org/10.1007/BF02679443 |z lizenzpflichtig |3 Volltext |
912 | |a GBV_USEFLAG_A | ||
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912 | |a GBV_ILN_22 | ||
912 | |a GBV_ILN_23 | ||
912 | |a GBV_ILN_24 | ||
912 | |a GBV_ILN_31 | ||
912 | |a GBV_ILN_32 | ||
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912 | |a GBV_ILN_40 | ||
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912 | |a GBV_ILN_63 | ||
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912 | |a GBV_ILN_70 | ||
912 | |a GBV_ILN_73 | ||
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912 | |a GBV_ILN_95 | ||
912 | |a GBV_ILN_100 | ||
912 | |a GBV_ILN_101 | ||
912 | |a GBV_ILN_105 | ||
912 | |a GBV_ILN_110 | ||
912 | |a GBV_ILN_120 | ||
912 | |a GBV_ILN_121 | ||
912 | |a GBV_ILN_138 | ||
912 | |a GBV_ILN_150 | ||
912 | |a GBV_ILN_151 | ||
912 | |a GBV_ILN_152 | ||
912 | |a GBV_ILN_161 | ||
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912 | |a GBV_ILN_187 | ||
912 | |a GBV_ILN_206 | ||
912 | |a GBV_ILN_213 | ||
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912 | |a GBV_ILN_374 | ||
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912 | |a GBV_ILN_636 | ||
912 | |a GBV_ILN_647 | ||
912 | |a GBV_ILN_702 | ||
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912 | |a GBV_ILN_2005 | ||
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912 | |a GBV_ILN_2010 | ||
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912 | |a GBV_ILN_2015 | ||
912 | |a GBV_ILN_2018 | ||
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912 | |a GBV_ILN_2021 | ||
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912 | |a GBV_ILN_2027 | ||
912 | |a GBV_ILN_2031 | ||
912 | |a GBV_ILN_2034 | ||
912 | |a GBV_ILN_2037 | ||
912 | |a GBV_ILN_2038 | ||
912 | |a GBV_ILN_2039 | ||
912 | |a GBV_ILN_2043 | ||
912 | |a GBV_ILN_2044 | ||
912 | |a GBV_ILN_2048 | ||
912 | |a GBV_ILN_2049 | ||
912 | |a GBV_ILN_2050 | ||
912 | |a GBV_ILN_2055 | ||
912 | |a GBV_ILN_2056 | ||
912 | |a GBV_ILN_2057 | ||
912 | |a GBV_ILN_2059 | ||
912 | |a GBV_ILN_2061 | ||
912 | |a GBV_ILN_2064 | ||
912 | |a GBV_ILN_2065 | ||
912 | |a GBV_ILN_2068 | ||
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912 | |a GBV_ILN_2093 | ||
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912 | |a GBV_ILN_2107 | ||
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912 | |a GBV_ILN_2111 | ||
912 | |a GBV_ILN_2112 | ||
912 | |a GBV_ILN_2113 | ||
912 | |a GBV_ILN_2116 | ||
912 | |a GBV_ILN_2118 | ||
912 | |a GBV_ILN_2119 | ||
912 | |a GBV_ILN_2122 | ||
912 | |a GBV_ILN_2129 | ||
912 | |a GBV_ILN_2143 | ||
912 | |a GBV_ILN_2144 | ||
912 | |a GBV_ILN_2147 | ||
912 | |a GBV_ILN_2148 | ||
912 | |a GBV_ILN_2152 | ||
912 | |a GBV_ILN_2153 | ||
912 | |a GBV_ILN_2158 | ||
912 | |a GBV_ILN_2188 | ||
912 | |a GBV_ILN_2190 | ||
912 | |a GBV_ILN_2193 | ||
912 | |a GBV_ILN_2232 | ||
912 | |a GBV_ILN_2336 | ||
912 | |a GBV_ILN_2446 | ||
912 | |a GBV_ILN_2470 | ||
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912 | |a GBV_ILN_2507 | ||
912 | |a GBV_ILN_2522 | ||
912 | |a GBV_ILN_2548 | ||
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912 | |a GBV_ILN_4307 | ||
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912 | |a GBV_ILN_4393 | ||
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951 | |a AR | ||
952 | |d 30 |j 1997 |e 2 |c 04 |h 113-119 |
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1997 |
publishDate |
1997 |
allfields |
10.1007/BF02679443 doi (DE-627)SPR002489074 (SPR)BF02679443-e DE-627 ger DE-627 rakwb eng Frances, M. verfasserin aut On covering problems of codes 1997 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag New York Inc 1997 Abstract LetC be a binary code of lengthn (i.e., a subset of {0, 1}n). TheCovering Radius of C is the smallest integerr such that each vector in {0, 1}n is at a distance at mostr from some code word. Our main result is that the decision problem associated with the Covering Radius of arbitrary binary codes is NP-complete. This result is established as follows. TheRadius of a binary codeC is the smallest integerr such thatC is contained in a radius-r ball of the Hamming metric space 〈{0, 1}n,d〉. It is known [K] that the problems of computing the Radius and the Covering Radius are equivalent. We show that the 3SAT problem is polynomially reducible to the Radius decision problem. A central tool in our reduction is a metrical characterization of the set ofdoubled vectors of length 2n: {v=(v1v2 …v2n) | ∀i:v2i=v2i−1}. We show that there is a setY ⊂ {0, 1}2n such that for everyv ε {0, 1}2n:v is doubled iffY is contained in the radius-n ball centered atv; moreover,Y can be constructed in time polynomial inn. Linear Code (dpeaa)DE-He213 Covering Problem (dpeaa)DE-He213 Code Word (dpeaa)DE-He213 Covering Radius (dpeaa)DE-He213 Minimum Radius (dpeaa)DE-He213 Litman, A. aut Enthalten in Theory of computing systems New York, NY : Springer, 1997 30(1997), 2 vom: Apr., Seite 113-119 (DE-627)254909728 (DE-600)1463181-7 1433-0490 nnns volume:30 year:1997 number:2 month:04 pages:113-119 https://dx.doi.org/10.1007/BF02679443 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 30 1997 2 04 113-119 |
spelling |
10.1007/BF02679443 doi (DE-627)SPR002489074 (SPR)BF02679443-e DE-627 ger DE-627 rakwb eng Frances, M. verfasserin aut On covering problems of codes 1997 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag New York Inc 1997 Abstract LetC be a binary code of lengthn (i.e., a subset of {0, 1}n). TheCovering Radius of C is the smallest integerr such that each vector in {0, 1}n is at a distance at mostr from some code word. Our main result is that the decision problem associated with the Covering Radius of arbitrary binary codes is NP-complete. This result is established as follows. TheRadius of a binary codeC is the smallest integerr such thatC is contained in a radius-r ball of the Hamming metric space 〈{0, 1}n,d〉. It is known [K] that the problems of computing the Radius and the Covering Radius are equivalent. We show that the 3SAT problem is polynomially reducible to the Radius decision problem. A central tool in our reduction is a metrical characterization of the set ofdoubled vectors of length 2n: {v=(v1v2 …v2n) | ∀i:v2i=v2i−1}. We show that there is a setY ⊂ {0, 1}2n such that for everyv ε {0, 1}2n:v is doubled iffY is contained in the radius-n ball centered atv; moreover,Y can be constructed in time polynomial inn. Linear Code (dpeaa)DE-He213 Covering Problem (dpeaa)DE-He213 Code Word (dpeaa)DE-He213 Covering Radius (dpeaa)DE-He213 Minimum Radius (dpeaa)DE-He213 Litman, A. aut Enthalten in Theory of computing systems New York, NY : Springer, 1997 30(1997), 2 vom: Apr., Seite 113-119 (DE-627)254909728 (DE-600)1463181-7 1433-0490 nnns volume:30 year:1997 number:2 month:04 pages:113-119 https://dx.doi.org/10.1007/BF02679443 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 30 1997 2 04 113-119 |
allfields_unstemmed |
10.1007/BF02679443 doi (DE-627)SPR002489074 (SPR)BF02679443-e DE-627 ger DE-627 rakwb eng Frances, M. verfasserin aut On covering problems of codes 1997 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag New York Inc 1997 Abstract LetC be a binary code of lengthn (i.e., a subset of {0, 1}n). TheCovering Radius of C is the smallest integerr such that each vector in {0, 1}n is at a distance at mostr from some code word. Our main result is that the decision problem associated with the Covering Radius of arbitrary binary codes is NP-complete. This result is established as follows. TheRadius of a binary codeC is the smallest integerr such thatC is contained in a radius-r ball of the Hamming metric space 〈{0, 1}n,d〉. It is known [K] that the problems of computing the Radius and the Covering Radius are equivalent. We show that the 3SAT problem is polynomially reducible to the Radius decision problem. A central tool in our reduction is a metrical characterization of the set ofdoubled vectors of length 2n: {v=(v1v2 …v2n) | ∀i:v2i=v2i−1}. We show that there is a setY ⊂ {0, 1}2n such that for everyv ε {0, 1}2n:v is doubled iffY is contained in the radius-n ball centered atv; moreover,Y can be constructed in time polynomial inn. Linear Code (dpeaa)DE-He213 Covering Problem (dpeaa)DE-He213 Code Word (dpeaa)DE-He213 Covering Radius (dpeaa)DE-He213 Minimum Radius (dpeaa)DE-He213 Litman, A. aut Enthalten in Theory of computing systems New York, NY : Springer, 1997 30(1997), 2 vom: Apr., Seite 113-119 (DE-627)254909728 (DE-600)1463181-7 1433-0490 nnns volume:30 year:1997 number:2 month:04 pages:113-119 https://dx.doi.org/10.1007/BF02679443 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 30 1997 2 04 113-119 |
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10.1007/BF02679443 doi (DE-627)SPR002489074 (SPR)BF02679443-e DE-627 ger DE-627 rakwb eng Frances, M. verfasserin aut On covering problems of codes 1997 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag New York Inc 1997 Abstract LetC be a binary code of lengthn (i.e., a subset of {0, 1}n). TheCovering Radius of C is the smallest integerr such that each vector in {0, 1}n is at a distance at mostr from some code word. Our main result is that the decision problem associated with the Covering Radius of arbitrary binary codes is NP-complete. This result is established as follows. TheRadius of a binary codeC is the smallest integerr such thatC is contained in a radius-r ball of the Hamming metric space 〈{0, 1}n,d〉. It is known [K] that the problems of computing the Radius and the Covering Radius are equivalent. We show that the 3SAT problem is polynomially reducible to the Radius decision problem. A central tool in our reduction is a metrical characterization of the set ofdoubled vectors of length 2n: {v=(v1v2 …v2n) | ∀i:v2i=v2i−1}. We show that there is a setY ⊂ {0, 1}2n such that for everyv ε {0, 1}2n:v is doubled iffY is contained in the radius-n ball centered atv; moreover,Y can be constructed in time polynomial inn. Linear Code (dpeaa)DE-He213 Covering Problem (dpeaa)DE-He213 Code Word (dpeaa)DE-He213 Covering Radius (dpeaa)DE-He213 Minimum Radius (dpeaa)DE-He213 Litman, A. aut Enthalten in Theory of computing systems New York, NY : Springer, 1997 30(1997), 2 vom: Apr., Seite 113-119 (DE-627)254909728 (DE-600)1463181-7 1433-0490 nnns volume:30 year:1997 number:2 month:04 pages:113-119 https://dx.doi.org/10.1007/BF02679443 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 30 1997 2 04 113-119 |
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10.1007/BF02679443 doi (DE-627)SPR002489074 (SPR)BF02679443-e DE-627 ger DE-627 rakwb eng Frances, M. verfasserin aut On covering problems of codes 1997 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag New York Inc 1997 Abstract LetC be a binary code of lengthn (i.e., a subset of {0, 1}n). TheCovering Radius of C is the smallest integerr such that each vector in {0, 1}n is at a distance at mostr from some code word. Our main result is that the decision problem associated with the Covering Radius of arbitrary binary codes is NP-complete. This result is established as follows. TheRadius of a binary codeC is the smallest integerr such thatC is contained in a radius-r ball of the Hamming metric space 〈{0, 1}n,d〉. It is known [K] that the problems of computing the Radius and the Covering Radius are equivalent. We show that the 3SAT problem is polynomially reducible to the Radius decision problem. A central tool in our reduction is a metrical characterization of the set ofdoubled vectors of length 2n: {v=(v1v2 …v2n) | ∀i:v2i=v2i−1}. We show that there is a setY ⊂ {0, 1}2n such that for everyv ε {0, 1}2n:v is doubled iffY is contained in the radius-n ball centered atv; moreover,Y can be constructed in time polynomial inn. Linear Code (dpeaa)DE-He213 Covering Problem (dpeaa)DE-He213 Code Word (dpeaa)DE-He213 Covering Radius (dpeaa)DE-He213 Minimum Radius (dpeaa)DE-He213 Litman, A. aut Enthalten in Theory of computing systems New York, NY : Springer, 1997 30(1997), 2 vom: Apr., Seite 113-119 (DE-627)254909728 (DE-600)1463181-7 1433-0490 nnns volume:30 year:1997 number:2 month:04 pages:113-119 https://dx.doi.org/10.1007/BF02679443 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 30 1997 2 04 113-119 |
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Enthalten in Theory of computing systems 30(1997), 2 vom: Apr., Seite 113-119 volume:30 year:1997 number:2 month:04 pages:113-119 |
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Frances, M. @@aut@@ Litman, A. @@aut@@ |
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TheCovering Radius of C is the smallest integerr such that each vector in {0, 1}n is at a distance at mostr from some code word. Our main result is that the decision problem associated with the Covering Radius of arbitrary binary codes is NP-complete. This result is established as follows. TheRadius of a binary codeC is the smallest integerr such thatC is contained in a radius-r ball of the Hamming metric space 〈{0, 1}n,d〉. It is known [K] that the problems of computing the Radius and the Covering Radius are equivalent. We show that the 3SAT problem is polynomially reducible to the Radius decision problem. A central tool in our reduction is a metrical characterization of the set ofdoubled vectors of length 2n: {v=(v1v2 …v2n) | ∀i:v2i=v2i−1}. We show that there is a setY ⊂ {0, 1}2n such that for everyv ε {0, 1}2n:v is doubled iffY is contained in the radius-n ball centered atv; moreover,Y can be constructed in time polynomial inn.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Linear Code</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Covering Problem</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Code Word</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Covering Radius</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Minimum Radius</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Litman, A.</subfield><subfield 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Frances, M. misc Linear Code misc Covering Problem misc Code Word misc Covering Radius misc Minimum Radius On covering problems of codes |
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On covering problems of codes Linear Code (dpeaa)DE-He213 Covering Problem (dpeaa)DE-He213 Code Word (dpeaa)DE-He213 Covering Radius (dpeaa)DE-He213 Minimum Radius (dpeaa)DE-He213 |
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on covering problems of codes |
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On covering problems of codes |
abstract |
Abstract LetC be a binary code of lengthn (i.e., a subset of {0, 1}n). TheCovering Radius of C is the smallest integerr such that each vector in {0, 1}n is at a distance at mostr from some code word. Our main result is that the decision problem associated with the Covering Radius of arbitrary binary codes is NP-complete. This result is established as follows. TheRadius of a binary codeC is the smallest integerr such thatC is contained in a radius-r ball of the Hamming metric space 〈{0, 1}n,d〉. It is known [K] that the problems of computing the Radius and the Covering Radius are equivalent. We show that the 3SAT problem is polynomially reducible to the Radius decision problem. A central tool in our reduction is a metrical characterization of the set ofdoubled vectors of length 2n: {v=(v1v2 …v2n) | ∀i:v2i=v2i−1}. We show that there is a setY ⊂ {0, 1}2n such that for everyv ε {0, 1}2n:v is doubled iffY is contained in the radius-n ball centered atv; moreover,Y can be constructed in time polynomial inn. © Springer-Verlag New York Inc 1997 |
abstractGer |
Abstract LetC be a binary code of lengthn (i.e., a subset of {0, 1}n). TheCovering Radius of C is the smallest integerr such that each vector in {0, 1}n is at a distance at mostr from some code word. Our main result is that the decision problem associated with the Covering Radius of arbitrary binary codes is NP-complete. This result is established as follows. TheRadius of a binary codeC is the smallest integerr such thatC is contained in a radius-r ball of the Hamming metric space 〈{0, 1}n,d〉. It is known [K] that the problems of computing the Radius and the Covering Radius are equivalent. We show that the 3SAT problem is polynomially reducible to the Radius decision problem. A central tool in our reduction is a metrical characterization of the set ofdoubled vectors of length 2n: {v=(v1v2 …v2n) | ∀i:v2i=v2i−1}. We show that there is a setY ⊂ {0, 1}2n such that for everyv ε {0, 1}2n:v is doubled iffY is contained in the radius-n ball centered atv; moreover,Y can be constructed in time polynomial inn. © Springer-Verlag New York Inc 1997 |
abstract_unstemmed |
Abstract LetC be a binary code of lengthn (i.e., a subset of {0, 1}n). TheCovering Radius of C is the smallest integerr such that each vector in {0, 1}n is at a distance at mostr from some code word. Our main result is that the decision problem associated with the Covering Radius of arbitrary binary codes is NP-complete. This result is established as follows. TheRadius of a binary codeC is the smallest integerr such thatC is contained in a radius-r ball of the Hamming metric space 〈{0, 1}n,d〉. It is known [K] that the problems of computing the Radius and the Covering Radius are equivalent. We show that the 3SAT problem is polynomially reducible to the Radius decision problem. A central tool in our reduction is a metrical characterization of the set ofdoubled vectors of length 2n: {v=(v1v2 …v2n) | ∀i:v2i=v2i−1}. We show that there is a setY ⊂ {0, 1}2n such that for everyv ε {0, 1}2n:v is doubled iffY is contained in the radius-n ball centered atv; moreover,Y can be constructed in time polynomial inn. © Springer-Verlag New York Inc 1997 |
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container_issue |
2 |
title_short |
On covering problems of codes |
url |
https://dx.doi.org/10.1007/BF02679443 |
remote_bool |
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author2 |
Litman, A. |
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doi_str |
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up_date |
2024-07-04T03:11:56.298Z |
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|
score |
7.39931 |