A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes

This paper presents a formula for the cardinality of a class of non-linear error correcting codes for Balanced Adjacent Deletions that are provided as an extension of standard deletion from the point of the view of Weyl groups. Furthermore, we show that the cardinality is approximately optimal over...
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Gespeichert in:

Autor*in:	Mori, Takehiko [verfasserIn] Hagiwara, Manabu [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Insertion/deletion codes Binary adjacent deletions Weyl groups Error-correcting codes Perfect codes Enumarative combinatorics

Übergeordnetes Werk:	Enthalten in: Discrete mathematics - Amsterdam [u.a.] : Elsevier, 1971, 343
Übergeordnetes Werk:	volume:343

DOI / URN:	10.1016/j.disc.2020.111852

Katalog-ID:	ELV003968618

Internformat


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100	1		\|a Mori, Takehiko \|e verfasserin \|4 aut
245	1	0	\|a A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes
264		1	\|c 2020
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337			\|a Computermedien \|b c \|2 rdamedia
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520			\|a This paper presents a formula for the cardinality of a class of non-linear error correcting codes for Balanced Adjacent Deletions that are provided as an extension of standard deletion from the point of the view of Weyl groups. Furthermore, we show that the cardinality is approximately optimal over any single BAD correcting codes. In other words, the ratio of the cardinality of the code and that of maximum cardinality BAD correcting code converges to 1 for sufficiently large length.
650		4	\|a Insertion/deletion codes
650		4	\|a Binary adjacent deletions
650		4	\|a Weyl groups
650		4	\|a Error-correcting codes
650		4	\|a Perfect codes
650		4	\|a Enumarative combinatorics
700	1		\|a Hagiwara, Manabu \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Discrete mathematics \|d Amsterdam [u.a.] : Elsevier, 1971 \|g 343 \|h Online-Ressource \|w (DE-627)266882439 \|w (DE-600)1468087-7 \|w (DE-576)09411059X \|7 nnns
773	1	8	\|g volume:343
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912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
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912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2056
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_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
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912			\|a GBV_ILN_4251
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
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912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
936	b	k	\|a 31.12 \|j Kombinatorik \|j Graphentheorie
936	b	k	\|a 31.20 \|j Algebra: Allgemeines
936	b	k	\|a 31.10 \|j Mathematische Logik \|j Mengenlehre
951			\|a AR
952			\|d 343

Indexfelder

author_variant	t m tm m h mh
matchkey_str	moritakehikohagiwaramanabu:2020----:nmetertcomladsmttcpiaiyfadnlte
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bklnumber	31.12 31.20 31.10
publishDate	2020
allfields	10.1016/j.disc.2020.111852 doi (DE-627)ELV003968618 (ELSEVIER)S0012-365X(20)30043-1 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl 31.20 bkl 31.10 bkl Mori, Takehiko verfasserin aut A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents a formula for the cardinality of a class of non-linear error correcting codes for Balanced Adjacent Deletions that are provided as an extension of standard deletion from the point of the view of Weyl groups. Furthermore, we show that the cardinality is approximately optimal over any single BAD correcting codes. In other words, the ratio of the cardinality of the code and that of maximum cardinality BAD correcting code converges to 1 for sufficiently large length. Insertion/deletion codes Binary adjacent deletions Weyl groups Error-correcting codes Perfect codes Enumarative combinatorics Hagiwara, Manabu verfasserin aut Enthalten in Discrete mathematics Amsterdam [u.a.] : Elsevier, 1971 343 Online-Ressource (DE-627)266882439 (DE-600)1468087-7 (DE-576)09411059X nnns volume:343 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie 31.20 Algebra: Allgemeines 31.10 Mathematische Logik Mengenlehre AR 343
spelling	10.1016/j.disc.2020.111852 doi (DE-627)ELV003968618 (ELSEVIER)S0012-365X(20)30043-1 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl 31.20 bkl 31.10 bkl Mori, Takehiko verfasserin aut A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents a formula for the cardinality of a class of non-linear error correcting codes for Balanced Adjacent Deletions that are provided as an extension of standard deletion from the point of the view of Weyl groups. Furthermore, we show that the cardinality is approximately optimal over any single BAD correcting codes. In other words, the ratio of the cardinality of the code and that of maximum cardinality BAD correcting code converges to 1 for sufficiently large length. Insertion/deletion codes Binary adjacent deletions Weyl groups Error-correcting codes Perfect codes Enumarative combinatorics Hagiwara, Manabu verfasserin aut Enthalten in Discrete mathematics Amsterdam [u.a.] : Elsevier, 1971 343 Online-Ressource (DE-627)266882439 (DE-600)1468087-7 (DE-576)09411059X nnns volume:343 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie 31.20 Algebra: Allgemeines 31.10 Mathematische Logik Mengenlehre AR 343
allfields_unstemmed	10.1016/j.disc.2020.111852 doi (DE-627)ELV003968618 (ELSEVIER)S0012-365X(20)30043-1 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl 31.20 bkl 31.10 bkl Mori, Takehiko verfasserin aut A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents a formula for the cardinality of a class of non-linear error correcting codes for Balanced Adjacent Deletions that are provided as an extension of standard deletion from the point of the view of Weyl groups. Furthermore, we show that the cardinality is approximately optimal over any single BAD correcting codes. In other words, the ratio of the cardinality of the code and that of maximum cardinality BAD correcting code converges to 1 for sufficiently large length. Insertion/deletion codes Binary adjacent deletions Weyl groups Error-correcting codes Perfect codes Enumarative combinatorics Hagiwara, Manabu verfasserin aut Enthalten in Discrete mathematics Amsterdam [u.a.] : Elsevier, 1971 343 Online-Ressource (DE-627)266882439 (DE-600)1468087-7 (DE-576)09411059X nnns volume:343 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie 31.20 Algebra: Allgemeines 31.10 Mathematische Logik Mengenlehre AR 343
allfieldsGer	10.1016/j.disc.2020.111852 doi (DE-627)ELV003968618 (ELSEVIER)S0012-365X(20)30043-1 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl 31.20 bkl 31.10 bkl Mori, Takehiko verfasserin aut A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents a formula for the cardinality of a class of non-linear error correcting codes for Balanced Adjacent Deletions that are provided as an extension of standard deletion from the point of the view of Weyl groups. Furthermore, we show that the cardinality is approximately optimal over any single BAD correcting codes. In other words, the ratio of the cardinality of the code and that of maximum cardinality BAD correcting code converges to 1 for sufficiently large length. Insertion/deletion codes Binary adjacent deletions Weyl groups Error-correcting codes Perfect codes Enumarative combinatorics Hagiwara, Manabu verfasserin aut Enthalten in Discrete mathematics Amsterdam [u.a.] : Elsevier, 1971 343 Online-Ressource (DE-627)266882439 (DE-600)1468087-7 (DE-576)09411059X nnns volume:343 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie 31.20 Algebra: Allgemeines 31.10 Mathematische Logik Mengenlehre AR 343
allfieldsSound	10.1016/j.disc.2020.111852 doi (DE-627)ELV003968618 (ELSEVIER)S0012-365X(20)30043-1 DE-627 ger DE-627 rda eng 510 DE-600 31.12 bkl 31.20 bkl 31.10 bkl Mori, Takehiko verfasserin aut A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper presents a formula for the cardinality of a class of non-linear error correcting codes for Balanced Adjacent Deletions that are provided as an extension of standard deletion from the point of the view of Weyl groups. Furthermore, we show that the cardinality is approximately optimal over any single BAD correcting codes. In other words, the ratio of the cardinality of the code and that of maximum cardinality BAD correcting code converges to 1 for sufficiently large length. Insertion/deletion codes Binary adjacent deletions Weyl groups Error-correcting codes Perfect codes Enumarative combinatorics Hagiwara, Manabu verfasserin aut Enthalten in Discrete mathematics Amsterdam [u.a.] : Elsevier, 1971 343 Online-Ressource (DE-627)266882439 (DE-600)1468087-7 (DE-576)09411059X nnns volume:343 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.12 Kombinatorik Graphentheorie 31.20 Algebra: Allgemeines 31.10 Mathematische Logik Mengenlehre AR 343
language	English
source	Enthalten in Discrete mathematics 343 volume:343
sourceStr	Enthalten in Discrete mathematics 343 volume:343
format_phy_str_mv	Article
bklname	Kombinatorik Graphentheorie Algebra: Allgemeines Mathematische Logik Mengenlehre
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topic_facet	Insertion/deletion codes Binary adjacent deletions Weyl groups Error-correcting codes Perfect codes Enumarative combinatorics
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author	Mori, Takehiko
spellingShingle	Mori, Takehiko ddc 510 bkl 31.12 bkl 31.20 bkl 31.10 misc Insertion/deletion codes misc Binary adjacent deletions misc Weyl groups misc Error-correcting codes misc Perfect codes misc Enumarative combinatorics A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes
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topic_title	510 DE-600 31.12 bkl 31.20 bkl 31.10 bkl A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes Insertion/deletion codes Binary adjacent deletions Weyl groups Error-correcting codes Perfect codes Enumarative combinatorics
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title	A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes
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title_full	A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes
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title_sort	a number theoretic formula and asymptotic optimality of cardinalities of bad correcting codes
title_auth	A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes
abstract	This paper presents a formula for the cardinality of a class of non-linear error correcting codes for Balanced Adjacent Deletions that are provided as an extension of standard deletion from the point of the view of Weyl groups. Furthermore, we show that the cardinality is approximately optimal over any single BAD correcting codes. In other words, the ratio of the cardinality of the code and that of maximum cardinality BAD correcting code converges to 1 for sufficiently large length.
abstractGer	This paper presents a formula for the cardinality of a class of non-linear error correcting codes for Balanced Adjacent Deletions that are provided as an extension of standard deletion from the point of the view of Weyl groups. Furthermore, we show that the cardinality is approximately optimal over any single BAD correcting codes. In other words, the ratio of the cardinality of the code and that of maximum cardinality BAD correcting code converges to 1 for sufficiently large length.
abstract_unstemmed	This paper presents a formula for the cardinality of a class of non-linear error correcting codes for Balanced Adjacent Deletions that are provided as an extension of standard deletion from the point of the view of Weyl groups. Furthermore, we show that the cardinality is approximately optimal over any single BAD correcting codes. In other words, the ratio of the cardinality of the code and that of maximum cardinality BAD correcting code converges to 1 for sufficiently large length.
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title_short	A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes
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up_date	2024-07-06T21:24:12.450Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV003968618</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230524142748.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230502s2020 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.disc.2020.111852</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV003968618</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0012-365X(20)30043-1</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.12</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.20</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.10</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Mori, Takehiko</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This paper presents a formula for the cardinality of a class of non-linear error correcting codes for Balanced Adjacent Deletions that are provided as an extension of standard deletion from the point of the view of Weyl groups. 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A number theoretic formula and asymptotic optimality of cardinalities of BAD correcting codes

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