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

Gespeichert in:

Autor*in:	Frances, M. [verfasserIn] Litman, A.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	1997

Schlagwörter:	Linear Code Covering Problem Code Word Covering Radius Minimum Radius

Anmerkung:	© Springer-Verlag New York Inc 1997

Übergeordnetes Werk:	Enthalten in: Theory of computing systems - New York, NY : Springer, 1997, 30(1997), 2 vom: Apr., Seite 113-119
Übergeordnetes Werk:	volume:30 ; year:1997 ; number:2 ; month:04 ; pages:113-119

Links:	Volltext

DOI / URN:	10.1007/BF02679443

Katalog-ID:	SPR002489074

Internformat


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100	1		\|a Frances, M. \|e verfasserin \|4 aut
245	1	0	\|a On covering problems of codes
264		1	\|c 1997
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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
912			\|a SYSFLAG_A
912			\|a GBV_SPRINGER
912			\|a GBV_ILN_11
912			\|a GBV_ILN_20
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
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
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
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_267
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_374
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_647
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2018
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
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
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
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
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_2808
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4277
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4346
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
912			\|a GBV_ILN_4753
951			\|a AR
952			\|d 30 \|j 1997 \|e 2 \|c 04 \|h 113-119

Indexfelder

author_variant	m f mf a l al
matchkey_str	article:14330490:1997----::noeigrbes
hierarchy_sort_str	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
allfieldsGer	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
allfieldsSound	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
language	English
source	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
sourceStr	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
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Linear Code Covering Problem Code Word Covering Radius Minimum Radius
isfreeaccess_bool	false
container_title	Theory of computing systems
authorswithroles_txt_mv	Frances, M. @@aut@@ Litman, A. @@aut@@
publishDateDaySort_date	1997-04-01T00:00:00Z
hierarchy_top_id	254909728
id	SPR002489074
language_de	englisch
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author	Frances, M.
spellingShingle	Frances, M. misc Linear Code misc Covering Problem misc Code Word misc Covering Radius misc Minimum Radius On covering problems of codes
authorStr	Frances, M.
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topic_title	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
topic	misc Linear Code misc Covering Problem misc Code Word misc Covering Radius misc Minimum Radius
topic_unstemmed	misc Linear Code misc Covering Problem misc Code Word misc Covering Radius misc Minimum Radius
topic_browse	misc Linear Code misc Covering Problem misc Code Word misc Covering Radius misc Minimum Radius
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	On covering problems of codes
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title_full	On covering problems of codes
author_sort	Frances, M.
journal	Theory of computing systems
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author_browse	Frances, M. Litman, A.
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author-letter	Frances, M.
doi_str_mv	10.1007/BF02679443
title_sort	on covering problems of codes
title_auth	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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title_short	On covering problems of codes
url	https://dx.doi.org/10.1007/BF02679443
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up_date	2024-07-04T03:11:56.298Z
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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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