Johnson graph codes
Abstract Array codes are the preferred codes for distributed storage, such that different rows in an array are stored at different nodes. Layered codes use a sparse format for stored arrays with a single parity check per column and no other parity checks. Remarkably, the simple structure of layered...
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Gespeichert in:
| Autor*in: |
Duursma, Iwan [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Designs, codes and cryptography - Springer US, 1991, 90(2022), 12 vom: 28. Feb., Seite 2923-2941 |
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| Übergeordnetes Werk: |
volume:90 ; year:2022 ; number:12 ; day:28 ; month:02 ; pages:2923-2941 |
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| DOI / URN: |
10.1007/s10623-021-01003-1 |
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OLC2079959166 |
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| 520 | |a Abstract Array codes are the preferred codes for distributed storage, such that different rows in an array are stored at different nodes. Layered codes use a sparse format for stored arrays with a single parity check per column and no other parity checks. Remarkably, the simple structure of layered codes is optimal when data is collected from all but one node. Codes that collect data from fewer nodes include improved layered codes, determinant codes, cascade codes and moulin codes. As our main result we show that the concatenation of layered codes with suitable outer codes achieves the performance of cascade and moulin codes which is conjectured to be optimal for general regenerating codes. The codes that we use as outer codes are in a new class of codes that we call Johnson graph codes. The codes have properties similar to those of Reed–Muller codes. In both cases the topological structure of the set of coordinates can be used to identify information sets and codewords of small weight. | ||
| 650 | 4 | |a Algebraic coding theory | |
| 650 | 4 | |a Codes for distributed storage | |
| 650 | 4 | |a Regenerating codes | |
| 650 | 4 | |a Johnson graph | |
| 650 | 4 | |a Multilinear algebra | |
| 650 | 4 | |a Determinants | |
| 700 | 1 | |a Li, Xiao |4 aut | |
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10.1007/s10623-021-01003-1 doi (DE-627)OLC2079959166 (DE-He213)s10623-021-01003-1-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Duursma, Iwan verfasserin (orcid)0000-0002-2436-3944 aut Johnson graph codes 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract Array codes are the preferred codes for distributed storage, such that different rows in an array are stored at different nodes. Layered codes use a sparse format for stored arrays with a single parity check per column and no other parity checks. Remarkably, the simple structure of layered codes is optimal when data is collected from all but one node. Codes that collect data from fewer nodes include improved layered codes, determinant codes, cascade codes and moulin codes. As our main result we show that the concatenation of layered codes with suitable outer codes achieves the performance of cascade and moulin codes which is conjectured to be optimal for general regenerating codes. The codes that we use as outer codes are in a new class of codes that we call Johnson graph codes. The codes have properties similar to those of Reed–Muller codes. In both cases the topological structure of the set of coordinates can be used to identify information sets and codewords of small weight. Algebraic coding theory Codes for distributed storage Regenerating codes Johnson graph Multilinear algebra Determinants Li, Xiao aut Enthalten in Designs, codes and cryptography Springer US, 1991 90(2022), 12 vom: 28. Feb., Seite 2923-2941 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:90 year:2022 number:12 day:28 month:02 pages:2923-2941 https://doi.org/10.1007/s10623-021-01003-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 90 2022 12 28 02 2923-2941 |
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10.1007/s10623-021-01003-1 doi (DE-627)OLC2079959166 (DE-He213)s10623-021-01003-1-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Duursma, Iwan verfasserin (orcid)0000-0002-2436-3944 aut Johnson graph codes 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract Array codes are the preferred codes for distributed storage, such that different rows in an array are stored at different nodes. Layered codes use a sparse format for stored arrays with a single parity check per column and no other parity checks. Remarkably, the simple structure of layered codes is optimal when data is collected from all but one node. Codes that collect data from fewer nodes include improved layered codes, determinant codes, cascade codes and moulin codes. As our main result we show that the concatenation of layered codes with suitable outer codes achieves the performance of cascade and moulin codes which is conjectured to be optimal for general regenerating codes. The codes that we use as outer codes are in a new class of codes that we call Johnson graph codes. The codes have properties similar to those of Reed–Muller codes. In both cases the topological structure of the set of coordinates can be used to identify information sets and codewords of small weight. Algebraic coding theory Codes for distributed storage Regenerating codes Johnson graph Multilinear algebra Determinants Li, Xiao aut Enthalten in Designs, codes and cryptography Springer US, 1991 90(2022), 12 vom: 28. Feb., Seite 2923-2941 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:90 year:2022 number:12 day:28 month:02 pages:2923-2941 https://doi.org/10.1007/s10623-021-01003-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 90 2022 12 28 02 2923-2941 |
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10.1007/s10623-021-01003-1 doi (DE-627)OLC2079959166 (DE-He213)s10623-021-01003-1-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Duursma, Iwan verfasserin (orcid)0000-0002-2436-3944 aut Johnson graph codes 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract Array codes are the preferred codes for distributed storage, such that different rows in an array are stored at different nodes. Layered codes use a sparse format for stored arrays with a single parity check per column and no other parity checks. Remarkably, the simple structure of layered codes is optimal when data is collected from all but one node. Codes that collect data from fewer nodes include improved layered codes, determinant codes, cascade codes and moulin codes. As our main result we show that the concatenation of layered codes with suitable outer codes achieves the performance of cascade and moulin codes which is conjectured to be optimal for general regenerating codes. The codes that we use as outer codes are in a new class of codes that we call Johnson graph codes. The codes have properties similar to those of Reed–Muller codes. In both cases the topological structure of the set of coordinates can be used to identify information sets and codewords of small weight. Algebraic coding theory Codes for distributed storage Regenerating codes Johnson graph Multilinear algebra Determinants Li, Xiao aut Enthalten in Designs, codes and cryptography Springer US, 1991 90(2022), 12 vom: 28. Feb., Seite 2923-2941 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:90 year:2022 number:12 day:28 month:02 pages:2923-2941 https://doi.org/10.1007/s10623-021-01003-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 90 2022 12 28 02 2923-2941 |
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10.1007/s10623-021-01003-1 doi (DE-627)OLC2079959166 (DE-He213)s10623-021-01003-1-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Duursma, Iwan verfasserin (orcid)0000-0002-2436-3944 aut Johnson graph codes 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract Array codes are the preferred codes for distributed storage, such that different rows in an array are stored at different nodes. Layered codes use a sparse format for stored arrays with a single parity check per column and no other parity checks. Remarkably, the simple structure of layered codes is optimal when data is collected from all but one node. Codes that collect data from fewer nodes include improved layered codes, determinant codes, cascade codes and moulin codes. As our main result we show that the concatenation of layered codes with suitable outer codes achieves the performance of cascade and moulin codes which is conjectured to be optimal for general regenerating codes. The codes that we use as outer codes are in a new class of codes that we call Johnson graph codes. The codes have properties similar to those of Reed–Muller codes. In both cases the topological structure of the set of coordinates can be used to identify information sets and codewords of small weight. Algebraic coding theory Codes for distributed storage Regenerating codes Johnson graph Multilinear algebra Determinants Li, Xiao aut Enthalten in Designs, codes and cryptography Springer US, 1991 90(2022), 12 vom: 28. Feb., Seite 2923-2941 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:90 year:2022 number:12 day:28 month:02 pages:2923-2941 https://doi.org/10.1007/s10623-021-01003-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 90 2022 12 28 02 2923-2941 |
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10.1007/s10623-021-01003-1 doi (DE-627)OLC2079959166 (DE-He213)s10623-021-01003-1-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Duursma, Iwan verfasserin (orcid)0000-0002-2436-3944 aut Johnson graph codes 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract Array codes are the preferred codes for distributed storage, such that different rows in an array are stored at different nodes. Layered codes use a sparse format for stored arrays with a single parity check per column and no other parity checks. Remarkably, the simple structure of layered codes is optimal when data is collected from all but one node. Codes that collect data from fewer nodes include improved layered codes, determinant codes, cascade codes and moulin codes. As our main result we show that the concatenation of layered codes with suitable outer codes achieves the performance of cascade and moulin codes which is conjectured to be optimal for general regenerating codes. The codes that we use as outer codes are in a new class of codes that we call Johnson graph codes. The codes have properties similar to those of Reed–Muller codes. In both cases the topological structure of the set of coordinates can be used to identify information sets and codewords of small weight. Algebraic coding theory Codes for distributed storage Regenerating codes Johnson graph Multilinear algebra Determinants Li, Xiao aut Enthalten in Designs, codes and cryptography Springer US, 1991 90(2022), 12 vom: 28. Feb., Seite 2923-2941 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:90 year:2022 number:12 day:28 month:02 pages:2923-2941 https://doi.org/10.1007/s10623-021-01003-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 90 2022 12 28 02 2923-2941 |
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Abstract Array codes are the preferred codes for distributed storage, such that different rows in an array are stored at different nodes. Layered codes use a sparse format for stored arrays with a single parity check per column and no other parity checks. Remarkably, the simple structure of layered codes is optimal when data is collected from all but one node. Codes that collect data from fewer nodes include improved layered codes, determinant codes, cascade codes and moulin codes. As our main result we show that the concatenation of layered codes with suitable outer codes achieves the performance of cascade and moulin codes which is conjectured to be optimal for general regenerating codes. The codes that we use as outer codes are in a new class of codes that we call Johnson graph codes. The codes have properties similar to those of Reed–Muller codes. In both cases the topological structure of the set of coordinates can be used to identify information sets and codewords of small weight. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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Abstract Array codes are the preferred codes for distributed storage, such that different rows in an array are stored at different nodes. Layered codes use a sparse format for stored arrays with a single parity check per column and no other parity checks. Remarkably, the simple structure of layered codes is optimal when data is collected from all but one node. Codes that collect data from fewer nodes include improved layered codes, determinant codes, cascade codes and moulin codes. As our main result we show that the concatenation of layered codes with suitable outer codes achieves the performance of cascade and moulin codes which is conjectured to be optimal for general regenerating codes. The codes that we use as outer codes are in a new class of codes that we call Johnson graph codes. The codes have properties similar to those of Reed–Muller codes. In both cases the topological structure of the set of coordinates can be used to identify information sets and codewords of small weight. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
| abstract_unstemmed |
Abstract Array codes are the preferred codes for distributed storage, such that different rows in an array are stored at different nodes. Layered codes use a sparse format for stored arrays with a single parity check per column and no other parity checks. Remarkably, the simple structure of layered codes is optimal when data is collected from all but one node. Codes that collect data from fewer nodes include improved layered codes, determinant codes, cascade codes and moulin codes. As our main result we show that the concatenation of layered codes with suitable outer codes achieves the performance of cascade and moulin codes which is conjectured to be optimal for general regenerating codes. The codes that we use as outer codes are in a new class of codes that we call Johnson graph codes. The codes have properties similar to those of Reed–Muller codes. In both cases the topological structure of the set of coordinates can be used to identify information sets and codewords of small weight. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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| title_short |
Johnson graph codes |
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https://doi.org/10.1007/s10623-021-01003-1 |
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false |
| author2 |
Li, Xiao |
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Li, Xiao |
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130994197 |
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| doi_str |
10.1007/s10623-021-01003-1 |
| up_date |
2024-07-04T02:32:07.132Z |
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1803613977586958336 |
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