New linear codes with few weights derived from Kloosterman sums

Linear codes with few weights have applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the works of Heng and Yue (2016) and Tan, Zhou, Tang and Helleseth (2017) , we extend Tan, Zhou, Tang and Helleseth's work to obtain a class of o...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Hu, Zhao [verfasserIn] Li, Nian [verfasserIn] Zeng, Xiangyong [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Kloosterman sums Linear codes Niho exponent Plotkin bound Weight distribution

Übergeordnetes Werk:	Enthalten in: No title available - 62
Übergeordnetes Werk:	volume:62

DOI / URN:	10.1016/j.ffa.2019.101608

Katalog-ID:	ELV003496872

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912			\|a GBV_ILN_2056
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912			\|a GBV_ILN_2113
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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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allfields	10.1016/j.ffa.2019.101608 doi (DE-627)ELV003496872 (ELSEVIER)S1071-5797(19)30111-X DE-627 ger DE-627 rda eng Hu, Zhao verfasserin aut New linear codes with few weights derived from Kloosterman sums 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Linear codes with few weights have applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the works of Heng and Yue (2016) and Tan, Zhou, Tang and Helleseth (2017) , we extend Tan, Zhou, Tang and Helleseth's work to obtain a class of optimal 1-weight binary linear codes, new classes of 2-weight and 3-weight p-ary linear codes and a class of 4-weight binary linear codes. The lengths and weight distributions of the t-weight linear codes, where t = 1 , 2 , 3 , are closed-form expressions of Kloosterman sums over finite prime fields, and are completely determined when p = 2 and p = 3 . Kloosterman sums Linear codes Niho exponent Plotkin bound Weight distribution Li, Nian verfasserin aut Zeng, Xiangyong verfasserin aut Enthalten in No title available 62 (DE-627)26687701X 1071-5797 nnns volume:62 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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 AR 62
spelling	10.1016/j.ffa.2019.101608 doi (DE-627)ELV003496872 (ELSEVIER)S1071-5797(19)30111-X DE-627 ger DE-627 rda eng Hu, Zhao verfasserin aut New linear codes with few weights derived from Kloosterman sums 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Linear codes with few weights have applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the works of Heng and Yue (2016) and Tan, Zhou, Tang and Helleseth (2017) , we extend Tan, Zhou, Tang and Helleseth's work to obtain a class of optimal 1-weight binary linear codes, new classes of 2-weight and 3-weight p-ary linear codes and a class of 4-weight binary linear codes. The lengths and weight distributions of the t-weight linear codes, where t = 1 , 2 , 3 , are closed-form expressions of Kloosterman sums over finite prime fields, and are completely determined when p = 2 and p = 3 . Kloosterman sums Linear codes Niho exponent Plotkin bound Weight distribution Li, Nian verfasserin aut Zeng, Xiangyong verfasserin aut Enthalten in No title available 62 (DE-627)26687701X 1071-5797 nnns volume:62 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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 AR 62
allfields_unstemmed	10.1016/j.ffa.2019.101608 doi (DE-627)ELV003496872 (ELSEVIER)S1071-5797(19)30111-X DE-627 ger DE-627 rda eng Hu, Zhao verfasserin aut New linear codes with few weights derived from Kloosterman sums 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Linear codes with few weights have applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the works of Heng and Yue (2016) and Tan, Zhou, Tang and Helleseth (2017) , we extend Tan, Zhou, Tang and Helleseth's work to obtain a class of optimal 1-weight binary linear codes, new classes of 2-weight and 3-weight p-ary linear codes and a class of 4-weight binary linear codes. The lengths and weight distributions of the t-weight linear codes, where t = 1 , 2 , 3 , are closed-form expressions of Kloosterman sums over finite prime fields, and are completely determined when p = 2 and p = 3 . Kloosterman sums Linear codes Niho exponent Plotkin bound Weight distribution Li, Nian verfasserin aut Zeng, Xiangyong verfasserin aut Enthalten in No title available 62 (DE-627)26687701X 1071-5797 nnns volume:62 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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 AR 62
allfieldsGer	10.1016/j.ffa.2019.101608 doi (DE-627)ELV003496872 (ELSEVIER)S1071-5797(19)30111-X DE-627 ger DE-627 rda eng Hu, Zhao verfasserin aut New linear codes with few weights derived from Kloosterman sums 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Linear codes with few weights have applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the works of Heng and Yue (2016) and Tan, Zhou, Tang and Helleseth (2017) , we extend Tan, Zhou, Tang and Helleseth's work to obtain a class of optimal 1-weight binary linear codes, new classes of 2-weight and 3-weight p-ary linear codes and a class of 4-weight binary linear codes. The lengths and weight distributions of the t-weight linear codes, where t = 1 , 2 , 3 , are closed-form expressions of Kloosterman sums over finite prime fields, and are completely determined when p = 2 and p = 3 . Kloosterman sums Linear codes Niho exponent Plotkin bound Weight distribution Li, Nian verfasserin aut Zeng, Xiangyong verfasserin aut Enthalten in No title available 62 (DE-627)26687701X 1071-5797 nnns volume:62 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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 AR 62
allfieldsSound	10.1016/j.ffa.2019.101608 doi (DE-627)ELV003496872 (ELSEVIER)S1071-5797(19)30111-X DE-627 ger DE-627 rda eng Hu, Zhao verfasserin aut New linear codes with few weights derived from Kloosterman sums 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Linear codes with few weights have applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the works of Heng and Yue (2016) and Tan, Zhou, Tang and Helleseth (2017) , we extend Tan, Zhou, Tang and Helleseth's work to obtain a class of optimal 1-weight binary linear codes, new classes of 2-weight and 3-weight p-ary linear codes and a class of 4-weight binary linear codes. The lengths and weight distributions of the t-weight linear codes, where t = 1 , 2 , 3 , are closed-form expressions of Kloosterman sums over finite prime fields, and are completely determined when p = 2 and p = 3 . Kloosterman sums Linear codes Niho exponent Plotkin bound Weight distribution Li, Nian verfasserin aut Zeng, Xiangyong verfasserin aut Enthalten in No title available 62 (DE-627)26687701X 1071-5797 nnns volume:62 GBV_USEFLAG_U SYSFLAG_U GBV_ELV 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 AR 62
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author	Hu, Zhao
spellingShingle	Hu, Zhao misc Kloosterman sums misc Linear codes misc Niho exponent misc Plotkin bound misc Weight distribution New linear codes with few weights derived from Kloosterman sums
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topic_title	New linear codes with few weights derived from Kloosterman sums Kloosterman sums Linear codes Niho exponent Plotkin bound Weight distribution
topic	misc Kloosterman sums misc Linear codes misc Niho exponent misc Plotkin bound misc Weight distribution
topic_unstemmed	misc Kloosterman sums misc Linear codes misc Niho exponent misc Plotkin bound misc Weight distribution
topic_browse	misc Kloosterman sums misc Linear codes misc Niho exponent misc Plotkin bound misc Weight distribution
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title	New linear codes with few weights derived from Kloosterman sums
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title_full	New linear codes with few weights derived from Kloosterman sums
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author_browse	Hu, Zhao Li, Nian Zeng, Xiangyong
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title_sort	new linear codes with few weights derived from kloosterman sums
title_auth	New linear codes with few weights derived from Kloosterman sums
abstract	Linear codes with few weights have applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the works of Heng and Yue (2016) and Tan, Zhou, Tang and Helleseth (2017) , we extend Tan, Zhou, Tang and Helleseth's work to obtain a class of optimal 1-weight binary linear codes, new classes of 2-weight and 3-weight p-ary linear codes and a class of 4-weight binary linear codes. The lengths and weight distributions of the t-weight linear codes, where t = 1 , 2 , 3 , are closed-form expressions of Kloosterman sums over finite prime fields, and are completely determined when p = 2 and p = 3 .
abstractGer	Linear codes with few weights have applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the works of Heng and Yue (2016) and Tan, Zhou, Tang and Helleseth (2017) , we extend Tan, Zhou, Tang and Helleseth's work to obtain a class of optimal 1-weight binary linear codes, new classes of 2-weight and 3-weight p-ary linear codes and a class of 4-weight binary linear codes. The lengths and weight distributions of the t-weight linear codes, where t = 1 , 2 , 3 , are closed-form expressions of Kloosterman sums over finite prime fields, and are completely determined when p = 2 and p = 3 .
abstract_unstemmed	Linear codes with few weights have applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the works of Heng and Yue (2016) and Tan, Zhou, Tang and Helleseth (2017) , we extend Tan, Zhou, Tang and Helleseth's work to obtain a class of optimal 1-weight binary linear codes, new classes of 2-weight and 3-weight p-ary linear codes and a class of 4-weight binary linear codes. The lengths and weight distributions of the t-weight linear codes, where t = 1 , 2 , 3 , are closed-form expressions of Kloosterman sums over finite prime fields, and are completely determined when p = 2 and p = 3 .
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title_short	New linear codes with few weights derived from Kloosterman sums
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author2	Li, Nian Zeng, Xiangyong
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doi_str	10.1016/j.ffa.2019.101608
up_date	2024-07-06T19:49:16.376Z
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In this paper, inspired by the works of Heng and Yue (2016) and Tan, Zhou, Tang and Helleseth (2017) , we extend Tan, Zhou, Tang and Helleseth's work to obtain a class of optimal 1-weight binary linear codes, new classes of 2-weight and 3-weight p-ary linear codes and a class of 4-weight binary linear codes. 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New linear codes with few weights derived from Kloosterman sums

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