On the automorphisms of generalized algebraic geometry codes

Abstract We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of %$N_1N_2%$-automorphism group of a GAG code in this class-that is, a subgroup of the automorphism gro...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Şenel, Engin [verfasserIn] Öke, Figen

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Geometric Goppa codes Generalized algebraic geometry codes Code automorphisms Automorphism groups of function fields Algebraic function fields

Anmerkung:	© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022

Übergeordnetes Werk:	Enthalten in: Designs, codes and cryptography - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1991, 90(2022), 6 vom: 30. Apr., Seite 1369-1379
Übergeordnetes Werk:	volume:90 ; year:2022 ; number:6 ; day:30 ; month:04 ; pages:1369-1379

Links:	Volltext

DOI / URN:	10.1007/s10623-022-01043-1

Katalog-ID:	SPR047181087

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520			\|a Abstract We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of %$N_1N_2%$-automorphism group of a GAG code in this class-that is, a subgroup of the automorphism group of the code. Then we determine a subgroup of the %$N_1N_2%$-automorphism group in the general case and the %$N_1N_2%$-automorphism group itself in the rational function field case. We also explicitly construct such a group. This paper presents a method to obtain similar results for the GAG codes that have more collections of places of the same degree in their construction.
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650		4	\|a Generalized algebraic geometry codes \|7 (dpeaa)DE-He213
650		4	\|a Code automorphisms \|7 (dpeaa)DE-He213
650		4	\|a Automorphism groups of function fields \|7 (dpeaa)DE-He213
650		4	\|a Algebraic function fields \|7 (dpeaa)DE-He213
700	1		\|a Öke, Figen \|4 aut
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allfields	10.1007/s10623-022-01043-1 doi (DE-627)SPR047181087 (SPR)s10623-022-01043-1-e DE-627 ger DE-627 rakwb eng Şenel, Engin verfasserin (orcid)0000-0002-1266-6702 aut On the automorphisms of generalized algebraic geometry codes 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of %$N_1N_2%$-automorphism group of a GAG code in this class-that is, a subgroup of the automorphism group of the code. Then we determine a subgroup of the %$N_1N_2%$-automorphism group in the general case and the %$N_1N_2%$-automorphism group itself in the rational function field case. We also explicitly construct such a group. This paper presents a method to obtain similar results for the GAG codes that have more collections of places of the same degree in their construction. Geometric Goppa codes (dpeaa)DE-He213 Generalized algebraic geometry codes (dpeaa)DE-He213 Code automorphisms (dpeaa)DE-He213 Automorphism groups of function fields (dpeaa)DE-He213 Algebraic function fields (dpeaa)DE-He213 Öke, Figen aut Enthalten in Designs, codes and cryptography Dordrecht [u.a.] : Springer Science + Business Media B.V, 1991 90(2022), 6 vom: 30. Apr., Seite 1369-1379 (DE-627)271350024 (DE-600)1479896-7 1573-7586 nnns volume:90 year:2022 number:6 day:30 month:04 pages:1369-1379 https://dx.doi.org/10.1007/s10623-022-01043-1 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_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 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_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_2118 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_2188 GBV_ILN_2190 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_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_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_4393 GBV_ILN_4700 AR 90 2022 6 30 04 1369-1379
spelling	10.1007/s10623-022-01043-1 doi (DE-627)SPR047181087 (SPR)s10623-022-01043-1-e DE-627 ger DE-627 rakwb eng Şenel, Engin verfasserin (orcid)0000-0002-1266-6702 aut On the automorphisms of generalized algebraic geometry codes 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of %$N_1N_2%$-automorphism group of a GAG code in this class-that is, a subgroup of the automorphism group of the code. Then we determine a subgroup of the %$N_1N_2%$-automorphism group in the general case and the %$N_1N_2%$-automorphism group itself in the rational function field case. We also explicitly construct such a group. This paper presents a method to obtain similar results for the GAG codes that have more collections of places of the same degree in their construction. Geometric Goppa codes (dpeaa)DE-He213 Generalized algebraic geometry codes (dpeaa)DE-He213 Code automorphisms (dpeaa)DE-He213 Automorphism groups of function fields (dpeaa)DE-He213 Algebraic function fields (dpeaa)DE-He213 Öke, Figen aut Enthalten in Designs, codes and cryptography Dordrecht [u.a.] : Springer Science + Business Media B.V, 1991 90(2022), 6 vom: 30. Apr., Seite 1369-1379 (DE-627)271350024 (DE-600)1479896-7 1573-7586 nnns volume:90 year:2022 number:6 day:30 month:04 pages:1369-1379 https://dx.doi.org/10.1007/s10623-022-01043-1 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_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 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_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_2118 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_2188 GBV_ILN_2190 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_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_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_4393 GBV_ILN_4700 AR 90 2022 6 30 04 1369-1379
allfields_unstemmed	10.1007/s10623-022-01043-1 doi (DE-627)SPR047181087 (SPR)s10623-022-01043-1-e DE-627 ger DE-627 rakwb eng Şenel, Engin verfasserin (orcid)0000-0002-1266-6702 aut On the automorphisms of generalized algebraic geometry codes 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of %$N_1N_2%$-automorphism group of a GAG code in this class-that is, a subgroup of the automorphism group of the code. Then we determine a subgroup of the %$N_1N_2%$-automorphism group in the general case and the %$N_1N_2%$-automorphism group itself in the rational function field case. We also explicitly construct such a group. This paper presents a method to obtain similar results for the GAG codes that have more collections of places of the same degree in their construction. Geometric Goppa codes (dpeaa)DE-He213 Generalized algebraic geometry codes (dpeaa)DE-He213 Code automorphisms (dpeaa)DE-He213 Automorphism groups of function fields (dpeaa)DE-He213 Algebraic function fields (dpeaa)DE-He213 Öke, Figen aut Enthalten in Designs, codes and cryptography Dordrecht [u.a.] : Springer Science + Business Media B.V, 1991 90(2022), 6 vom: 30. Apr., Seite 1369-1379 (DE-627)271350024 (DE-600)1479896-7 1573-7586 nnns volume:90 year:2022 number:6 day:30 month:04 pages:1369-1379 https://dx.doi.org/10.1007/s10623-022-01043-1 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_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 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_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_2118 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_2188 GBV_ILN_2190 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_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_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_4393 GBV_ILN_4700 AR 90 2022 6 30 04 1369-1379
allfieldsGer	10.1007/s10623-022-01043-1 doi (DE-627)SPR047181087 (SPR)s10623-022-01043-1-e DE-627 ger DE-627 rakwb eng Şenel, Engin verfasserin (orcid)0000-0002-1266-6702 aut On the automorphisms of generalized algebraic geometry codes 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of %$N_1N_2%$-automorphism group of a GAG code in this class-that is, a subgroup of the automorphism group of the code. Then we determine a subgroup of the %$N_1N_2%$-automorphism group in the general case and the %$N_1N_2%$-automorphism group itself in the rational function field case. We also explicitly construct such a group. This paper presents a method to obtain similar results for the GAG codes that have more collections of places of the same degree in their construction. Geometric Goppa codes (dpeaa)DE-He213 Generalized algebraic geometry codes (dpeaa)DE-He213 Code automorphisms (dpeaa)DE-He213 Automorphism groups of function fields (dpeaa)DE-He213 Algebraic function fields (dpeaa)DE-He213 Öke, Figen aut Enthalten in Designs, codes and cryptography Dordrecht [u.a.] : Springer Science + Business Media B.V, 1991 90(2022), 6 vom: 30. Apr., Seite 1369-1379 (DE-627)271350024 (DE-600)1479896-7 1573-7586 nnns volume:90 year:2022 number:6 day:30 month:04 pages:1369-1379 https://dx.doi.org/10.1007/s10623-022-01043-1 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_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 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_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_2118 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_2188 GBV_ILN_2190 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_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_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_4393 GBV_ILN_4700 AR 90 2022 6 30 04 1369-1379
allfieldsSound	10.1007/s10623-022-01043-1 doi (DE-627)SPR047181087 (SPR)s10623-022-01043-1-e DE-627 ger DE-627 rakwb eng Şenel, Engin verfasserin (orcid)0000-0002-1266-6702 aut On the automorphisms of generalized algebraic geometry codes 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of %$N_1N_2%$-automorphism group of a GAG code in this class-that is, a subgroup of the automorphism group of the code. Then we determine a subgroup of the %$N_1N_2%$-automorphism group in the general case and the %$N_1N_2%$-automorphism group itself in the rational function field case. We also explicitly construct such a group. This paper presents a method to obtain similar results for the GAG codes that have more collections of places of the same degree in their construction. Geometric Goppa codes (dpeaa)DE-He213 Generalized algebraic geometry codes (dpeaa)DE-He213 Code automorphisms (dpeaa)DE-He213 Automorphism groups of function fields (dpeaa)DE-He213 Algebraic function fields (dpeaa)DE-He213 Öke, Figen aut Enthalten in Designs, codes and cryptography Dordrecht [u.a.] : Springer Science + Business Media B.V, 1991 90(2022), 6 vom: 30. Apr., Seite 1369-1379 (DE-627)271350024 (DE-600)1479896-7 1573-7586 nnns volume:90 year:2022 number:6 day:30 month:04 pages:1369-1379 https://dx.doi.org/10.1007/s10623-022-01043-1 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_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 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_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_2118 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_2188 GBV_ILN_2190 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_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_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_4393 GBV_ILN_4700 AR 90 2022 6 30 04 1369-1379
language	English
source	Enthalten in Designs, codes and cryptography 90(2022), 6 vom: 30. Apr., Seite 1369-1379 volume:90 year:2022 number:6 day:30 month:04 pages:1369-1379
sourceStr	Enthalten in Designs, codes and cryptography 90(2022), 6 vom: 30. Apr., Seite 1369-1379 volume:90 year:2022 number:6 day:30 month:04 pages:1369-1379
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Geometric Goppa codes Generalized algebraic geometry codes Code automorphisms Automorphism groups of function fields Algebraic function fields
isfreeaccess_bool	false
container_title	Designs, codes and cryptography
authorswithroles_txt_mv	Şenel, Engin @@aut@@ Öke, Figen @@aut@@
publishDateDaySort_date	2022-04-30T00:00:00Z
hierarchy_top_id	271350024
id	SPR047181087
language_de	englisch
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author	Şenel, Engin
spellingShingle	Şenel, Engin misc Geometric Goppa codes misc Generalized algebraic geometry codes misc Code automorphisms misc Automorphism groups of function fields misc Algebraic function fields On the automorphisms of generalized algebraic geometry codes
authorStr	Şenel, Engin
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topic_title	On the automorphisms of generalized algebraic geometry codes Geometric Goppa codes (dpeaa)DE-He213 Generalized algebraic geometry codes (dpeaa)DE-He213 Code automorphisms (dpeaa)DE-He213 Automorphism groups of function fields (dpeaa)DE-He213 Algebraic function fields (dpeaa)DE-He213
topic	misc Geometric Goppa codes misc Generalized algebraic geometry codes misc Code automorphisms misc Automorphism groups of function fields misc Algebraic function fields
topic_unstemmed	misc Geometric Goppa codes misc Generalized algebraic geometry codes misc Code automorphisms misc Automorphism groups of function fields misc Algebraic function fields
topic_browse	misc Geometric Goppa codes misc Generalized algebraic geometry codes misc Code automorphisms misc Automorphism groups of function fields misc Algebraic function fields
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title	On the automorphisms of generalized algebraic geometry codes
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title_full	On the automorphisms of generalized algebraic geometry codes
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title_sort	on the automorphisms of generalized algebraic geometry codes
title_auth	On the automorphisms of generalized algebraic geometry codes
abstract	Abstract We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of %$N_1N_2%$-automorphism group of a GAG code in this class-that is, a subgroup of the automorphism group of the code. Then we determine a subgroup of the %$N_1N_2%$-automorphism group in the general case and the %$N_1N_2%$-automorphism group itself in the rational function field case. We also explicitly construct such a group. This paper presents a method to obtain similar results for the GAG codes that have more collections of places of the same degree in their construction. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022
abstractGer	Abstract We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of %$N_1N_2%$-automorphism group of a GAG code in this class-that is, a subgroup of the automorphism group of the code. Then we determine a subgroup of the %$N_1N_2%$-automorphism group in the general case and the %$N_1N_2%$-automorphism group itself in the rational function field case. We also explicitly construct such a group. This paper presents a method to obtain similar results for the GAG codes that have more collections of places of the same degree in their construction. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022
abstract_unstemmed	Abstract We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of %$N_1N_2%$-automorphism group of a GAG code in this class-that is, a subgroup of the automorphism group of the code. Then we determine a subgroup of the %$N_1N_2%$-automorphism group in the general case and the %$N_1N_2%$-automorphism group itself in the rational function field case. We also explicitly construct such a group. This paper presents a method to obtain similar results for the GAG codes that have more collections of places of the same degree in their construction. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022
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title_short	On the automorphisms of generalized algebraic geometry codes
url	https://dx.doi.org/10.1007/s10623-022-01043-1
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We introduce the concept of %$N_1N_2%$-automorphism group of a GAG code in this class-that is, a subgroup of the automorphism group of the code. Then we determine a subgroup of the %$N_1N_2%$-automorphism group in the general case and the %$N_1N_2%$-automorphism group itself in the rational function field case. We also explicitly construct such a group. 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On the automorphisms of generalized algebraic geometry codes

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