Characterization of the automorphism group of quaternary linear Hadamard codes
Abstract A quaternary linear Hadamard code $${\mathcal{C}}$$ is a code over $${\mathbb{Z}_4}$$ such that, under the Gray map, gives a binary Hadamard code. The permutation automorphism group of a quaternary linear code $${\mathcal{C}}$$ of length n is defined as $${{\rm PAut}(\mathcal{C}) = \{\sigma...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Pernas, Jaume [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2012 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, LLC 2012 |
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| Übergeordnetes Werk: |
Enthalten in: Designs, codes and cryptography - Springer US, 1991, 70(2012), 1-2 vom: 25. Mai, Seite 105-115 |
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| Übergeordnetes Werk: |
volume:70 ; year:2012 ; number:1-2 ; day:25 ; month:05 ; pages:105-115 |
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| DOI / URN: |
10.1007/s10623-012-9678-2 |
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| 520 | |a Abstract A quaternary linear Hadamard code $${\mathcal{C}}$$ is a code over $${\mathbb{Z}_4}$$ such that, under the Gray map, gives a binary Hadamard code. The permutation automorphism group of a quaternary linear code $${\mathcal{C}}$$ of length n is defined as $${{\rm PAut}(\mathcal{C}) = \{\sigma \in S_{n} : \sigma(\mathcal{C}) = \mathcal{C}\}}$$. In this paper, the order of the permutation automorphism group of a family of quaternary linear Hadamard codes is established. Moreover, these groups are completely characterized by computing the orbits of the action of $${{\rm PAut}(\mathcal{C})}$$ on $${\mathcal{C}}$$ and by giving the generators of the group. Since the dual of a Hadamard code is an extended 1-perfect code in the quaternary sense, the permutation automorphism group of these codes is also computed. | ||
| 650 | 4 | |a Quaternary linear codes | |
| 650 | 4 | |a Hadamard codes | |
| 650 | 4 | |a 1-Perfect codes | |
| 650 | 4 | |a Permutation automorphism group | |
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| 700 | 1 | |a Villanueva, Mercè |4 aut | |
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10.1007/s10623-012-9678-2 doi (DE-627)OLC2027293833 (DE-He213)s10623-012-9678-2-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Pernas, Jaume verfasserin aut Characterization of the automorphism group of quaternary linear Hadamard codes 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2012 Abstract A quaternary linear Hadamard code $${\mathcal{C}}$$ is a code over $${\mathbb{Z}_4}$$ such that, under the Gray map, gives a binary Hadamard code. The permutation automorphism group of a quaternary linear code $${\mathcal{C}}$$ of length n is defined as $${{\rm PAut}(\mathcal{C}) = \{\sigma \in S_{n} : \sigma(\mathcal{C}) = \mathcal{C}\}}$$. In this paper, the order of the permutation automorphism group of a family of quaternary linear Hadamard codes is established. Moreover, these groups are completely characterized by computing the orbits of the action of $${{\rm PAut}(\mathcal{C})}$$ on $${\mathcal{C}}$$ and by giving the generators of the group. Since the dual of a Hadamard code is an extended 1-perfect code in the quaternary sense, the permutation automorphism group of these codes is also computed. Quaternary linear codes Hadamard codes 1-Perfect codes Permutation automorphism group Pujol, Jaume aut Villanueva, Mercè aut Enthalten in Designs, codes and cryptography Springer US, 1991 70(2012), 1-2 vom: 25. Mai, Seite 105-115 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:70 year:2012 number:1-2 day:25 month:05 pages:105-115 https://doi.org/10.1007/s10623-012-9678-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 AR 70 2012 1-2 25 05 105-115 |
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10.1007/s10623-012-9678-2 doi (DE-627)OLC2027293833 (DE-He213)s10623-012-9678-2-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Pernas, Jaume verfasserin aut Characterization of the automorphism group of quaternary linear Hadamard codes 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2012 Abstract A quaternary linear Hadamard code $${\mathcal{C}}$$ is a code over $${\mathbb{Z}_4}$$ such that, under the Gray map, gives a binary Hadamard code. The permutation automorphism group of a quaternary linear code $${\mathcal{C}}$$ of length n is defined as $${{\rm PAut}(\mathcal{C}) = \{\sigma \in S_{n} : \sigma(\mathcal{C}) = \mathcal{C}\}}$$. In this paper, the order of the permutation automorphism group of a family of quaternary linear Hadamard codes is established. Moreover, these groups are completely characterized by computing the orbits of the action of $${{\rm PAut}(\mathcal{C})}$$ on $${\mathcal{C}}$$ and by giving the generators of the group. Since the dual of a Hadamard code is an extended 1-perfect code in the quaternary sense, the permutation automorphism group of these codes is also computed. Quaternary linear codes Hadamard codes 1-Perfect codes Permutation automorphism group Pujol, Jaume aut Villanueva, Mercè aut Enthalten in Designs, codes and cryptography Springer US, 1991 70(2012), 1-2 vom: 25. Mai, Seite 105-115 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:70 year:2012 number:1-2 day:25 month:05 pages:105-115 https://doi.org/10.1007/s10623-012-9678-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 AR 70 2012 1-2 25 05 105-115 |
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10.1007/s10623-012-9678-2 doi (DE-627)OLC2027293833 (DE-He213)s10623-012-9678-2-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Pernas, Jaume verfasserin aut Characterization of the automorphism group of quaternary linear Hadamard codes 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2012 Abstract A quaternary linear Hadamard code $${\mathcal{C}}$$ is a code over $${\mathbb{Z}_4}$$ such that, under the Gray map, gives a binary Hadamard code. The permutation automorphism group of a quaternary linear code $${\mathcal{C}}$$ of length n is defined as $${{\rm PAut}(\mathcal{C}) = \{\sigma \in S_{n} : \sigma(\mathcal{C}) = \mathcal{C}\}}$$. In this paper, the order of the permutation automorphism group of a family of quaternary linear Hadamard codes is established. Moreover, these groups are completely characterized by computing the orbits of the action of $${{\rm PAut}(\mathcal{C})}$$ on $${\mathcal{C}}$$ and by giving the generators of the group. Since the dual of a Hadamard code is an extended 1-perfect code in the quaternary sense, the permutation automorphism group of these codes is also computed. Quaternary linear codes Hadamard codes 1-Perfect codes Permutation automorphism group Pujol, Jaume aut Villanueva, Mercè aut Enthalten in Designs, codes and cryptography Springer US, 1991 70(2012), 1-2 vom: 25. Mai, Seite 105-115 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:70 year:2012 number:1-2 day:25 month:05 pages:105-115 https://doi.org/10.1007/s10623-012-9678-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 AR 70 2012 1-2 25 05 105-115 |
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10.1007/s10623-012-9678-2 doi (DE-627)OLC2027293833 (DE-He213)s10623-012-9678-2-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Pernas, Jaume verfasserin aut Characterization of the automorphism group of quaternary linear Hadamard codes 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2012 Abstract A quaternary linear Hadamard code $${\mathcal{C}}$$ is a code over $${\mathbb{Z}_4}$$ such that, under the Gray map, gives a binary Hadamard code. The permutation automorphism group of a quaternary linear code $${\mathcal{C}}$$ of length n is defined as $${{\rm PAut}(\mathcal{C}) = \{\sigma \in S_{n} : \sigma(\mathcal{C}) = \mathcal{C}\}}$$. In this paper, the order of the permutation automorphism group of a family of quaternary linear Hadamard codes is established. Moreover, these groups are completely characterized by computing the orbits of the action of $${{\rm PAut}(\mathcal{C})}$$ on $${\mathcal{C}}$$ and by giving the generators of the group. Since the dual of a Hadamard code is an extended 1-perfect code in the quaternary sense, the permutation automorphism group of these codes is also computed. Quaternary linear codes Hadamard codes 1-Perfect codes Permutation automorphism group Pujol, Jaume aut Villanueva, Mercè aut Enthalten in Designs, codes and cryptography Springer US, 1991 70(2012), 1-2 vom: 25. Mai, Seite 105-115 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:70 year:2012 number:1-2 day:25 month:05 pages:105-115 https://doi.org/10.1007/s10623-012-9678-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 AR 70 2012 1-2 25 05 105-115 |
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characterization of the automorphism group of quaternary linear hadamard codes |
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Characterization of the automorphism group of quaternary linear Hadamard codes |
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Abstract A quaternary linear Hadamard code $${\mathcal{C}}$$ is a code over $${\mathbb{Z}_4}$$ such that, under the Gray map, gives a binary Hadamard code. The permutation automorphism group of a quaternary linear code $${\mathcal{C}}$$ of length n is defined as $${{\rm PAut}(\mathcal{C}) = \{\sigma \in S_{n} : \sigma(\mathcal{C}) = \mathcal{C}\}}$$. In this paper, the order of the permutation automorphism group of a family of quaternary linear Hadamard codes is established. Moreover, these groups are completely characterized by computing the orbits of the action of $${{\rm PAut}(\mathcal{C})}$$ on $${\mathcal{C}}$$ and by giving the generators of the group. Since the dual of a Hadamard code is an extended 1-perfect code in the quaternary sense, the permutation automorphism group of these codes is also computed. © Springer Science+Business Media, LLC 2012 |
| abstractGer |
Abstract A quaternary linear Hadamard code $${\mathcal{C}}$$ is a code over $${\mathbb{Z}_4}$$ such that, under the Gray map, gives a binary Hadamard code. The permutation automorphism group of a quaternary linear code $${\mathcal{C}}$$ of length n is defined as $${{\rm PAut}(\mathcal{C}) = \{\sigma \in S_{n} : \sigma(\mathcal{C}) = \mathcal{C}\}}$$. In this paper, the order of the permutation automorphism group of a family of quaternary linear Hadamard codes is established. Moreover, these groups are completely characterized by computing the orbits of the action of $${{\rm PAut}(\mathcal{C})}$$ on $${\mathcal{C}}$$ and by giving the generators of the group. Since the dual of a Hadamard code is an extended 1-perfect code in the quaternary sense, the permutation automorphism group of these codes is also computed. © Springer Science+Business Media, LLC 2012 |
| abstract_unstemmed |
Abstract A quaternary linear Hadamard code $${\mathcal{C}}$$ is a code over $${\mathbb{Z}_4}$$ such that, under the Gray map, gives a binary Hadamard code. The permutation automorphism group of a quaternary linear code $${\mathcal{C}}$$ of length n is defined as $${{\rm PAut}(\mathcal{C}) = \{\sigma \in S_{n} : \sigma(\mathcal{C}) = \mathcal{C}\}}$$. In this paper, the order of the permutation automorphism group of a family of quaternary linear Hadamard codes is established. Moreover, these groups are completely characterized by computing the orbits of the action of $${{\rm PAut}(\mathcal{C})}$$ on $${\mathcal{C}}$$ and by giving the generators of the group. Since the dual of a Hadamard code is an extended 1-perfect code in the quaternary sense, the permutation automorphism group of these codes is also computed. © Springer Science+Business Media, LLC 2012 |
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Characterization of the automorphism group of quaternary linear Hadamard codes |
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Pujol, Jaume Villanueva, Mercè |
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