-
Previous Article
Constructions of asymptotically optimal codebooks with respect to Welch bound and Levenshtein bound
- AMC Home
- This Issue
-
Next Article
Generalized Hamming weights of toric codes over hypersimplices and squarefree affine evaluation codes
Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.
Readers can access Online First articles via the “Online First” tab for the selected journal.
Degenerate flag varieties in network coding
RWTH Aachen University, 52056 Aachen, Germany |
Building upon the application of flags to network coding introduced in [
References:
| [1] |
G. Cerulli Irelli, X. Fang, E. Feigin, G. Fourier and R. Reineke,
Linear degenerations of flag varieties, Math. Z., 287 (2017), 615-654.
doi: 10.1007/s00209-016-1839-y. |
| [2] |
E. Feigin,
$\mathbb{G}_a^M$ degeneration of flag varieties, Selecta Math. (N.S.), 18 (2012), 513-537.
doi: 10.1007/s00029-011-0084-9. |
| [3] |
E. Feigin, G. Fourier and P. Littelmann,
PBW filtration and bases for irreducible modules in type $ {\mathbb{A}} _n$, Transform. Groups, 16 (2011), 71-89.
doi: 10.1007/s00031-010-9115-4. |
| [4] |
G. C. Irelli and M. Lanini,
Degenerate flag varieties of type $ {\mathbb{A}} $ and $ {\mathbb{C}} $ are schubert varieties, Int. Math. Research Notices, 2015 (2015), 6353-6374.
doi: 10.1093/imrn/rnu128. |
| [5] |
R. Kötter and F. R. Kschischang,
Coding for errors and erasures in random network coding, IEEE Trans. Inform., 54 (2008), 3579-3591.
doi: 10.1109/TIT.2008.926449. |
| [6] |
D. Liebhold, G. Nebe and A. Vazquez-Castro,
Network coding with flags, Des. Codes Cryptogr., 86 (2018), 269-284.
doi: 10.1007/s10623-017-0361-5. |
| [7] |
D. Liebhold, Flag Codes With Application to Network Coding, PhD Thesis, RWTH Aachen 2019. |
| [8] |
A. Ravagnani,
Rank-metric codes and their duality theory, Des. Codes Cryptogr., 80 (2016), 197-216.
doi: 10.1007/s10623-015-0077-3. |
| [9] |
D. Silva, F. R. Kschischang and R. Kötter,
A rank-metric approach to error control in random network coding, IEEE Trans. Inform. Theory, 54 (2008), 3951-3967.
doi: 10.1109/TIT.2008.928291. |
show all references
References:
| [1] |
G. Cerulli Irelli, X. Fang, E. Feigin, G. Fourier and R. Reineke,
Linear degenerations of flag varieties, Math. Z., 287 (2017), 615-654.
doi: 10.1007/s00209-016-1839-y. |
| [2] |
E. Feigin,
$\mathbb{G}_a^M$ degeneration of flag varieties, Selecta Math. (N.S.), 18 (2012), 513-537.
doi: 10.1007/s00029-011-0084-9. |
| [3] |
E. Feigin, G. Fourier and P. Littelmann,
PBW filtration and bases for irreducible modules in type $ {\mathbb{A}} _n$, Transform. Groups, 16 (2011), 71-89.
doi: 10.1007/s00031-010-9115-4. |
| [4] |
G. C. Irelli and M. Lanini,
Degenerate flag varieties of type $ {\mathbb{A}} $ and $ {\mathbb{C}} $ are schubert varieties, Int. Math. Research Notices, 2015 (2015), 6353-6374.
doi: 10.1093/imrn/rnu128. |
| [5] |
R. Kötter and F. R. Kschischang,
Coding for errors and erasures in random network coding, IEEE Trans. Inform., 54 (2008), 3579-3591.
doi: 10.1109/TIT.2008.926449. |
| [6] |
D. Liebhold, G. Nebe and A. Vazquez-Castro,
Network coding with flags, Des. Codes Cryptogr., 86 (2018), 269-284.
doi: 10.1007/s10623-017-0361-5. |
| [7] |
D. Liebhold, Flag Codes With Application to Network Coding, PhD Thesis, RWTH Aachen 2019. |
| [8] |
A. Ravagnani,
Rank-metric codes and their duality theory, Des. Codes Cryptogr., 80 (2016), 197-216.
doi: 10.1007/s10623-015-0077-3. |
| [9] |
D. Silva, F. R. Kschischang and R. Kötter,
A rank-metric approach to error control in random network coding, IEEE Trans. Inform. Theory, 54 (2008), 3951-3967.
doi: 10.1109/TIT.2008.928291. |
| [1] |
John Sheekey. A new family of linear maximum rank distance codes. Advances in Mathematics of Communications, 2016, 10 (3) : 475-488. doi: 10.3934/amc.2016019 |
| [2] |
Umberto Martínez-Peñas. Rank equivalent and rank degenerate skew cyclic codes. Advances in Mathematics of Communications, 2017, 11 (2) : 267-282. doi: 10.3934/amc.2017018 |
| [3] |
Yujuan Li, Guizhen Zhu. On the error distance of extended Reed-Solomon codes. Advances in Mathematics of Communications, 2016, 10 (2) : 413-427. doi: 10.3934/amc.2016015 |
| [4] |
Yanyan Gao, Qin Yue, Xinmei Huang, Yun Yang. Two classes of cyclic extended double-error-correcting Goppa codes. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2022003 |
| [5] |
Muhammad Ajmal, Xiande Zhang. New optimal error-correcting codes for crosstalk avoidance in on-chip data buses. Advances in Mathematics of Communications, 2021, 15 (3) : 487-506. doi: 10.3934/amc.2020078 |
| [6] |
René B. Christensen, Carlos Munuera, Francisco R. F. Pereira, Diego Ruano. An algorithmic approach to entanglement-assisted quantum error-correcting codes from the Hermitian curve. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2021072 |
| [7] |
Thiago Ferraiol, Mauro Patrão, Lucas Seco. Jordan decomposition and dynamics on flag manifolds. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 923-947. doi: 10.3934/dcds.2010.26.923 |
| [8] |
Kamil Otal, Ferruh Özbudak. Explicit constructions of some non-Gabidulin linear maximum rank distance codes. Advances in Mathematics of Communications, 2016, 10 (3) : 589-600. doi: 10.3934/amc.2016028 |
| [9] |
Negin Karimi, Ahmad Yousefian Darani, Marcus Greferath. Correcting adversarial errors with generalized regenerating codes. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2022005 |
| [10] |
Anna-Lena Horlemann-Trautmann, Kyle Marshall. New criteria for MRD and Gabidulin codes and some Rank-Metric code constructions. Advances in Mathematics of Communications, 2017, 11 (3) : 533-548. doi: 10.3934/amc.2017042 |
| [11] |
Rakhi Pratihar, Tovohery Hajatiana Randrianarisoa. Constructions of optimal rank-metric codes from automorphisms of rational function fields. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2022034 |
| [12] |
Michael Braun. On lattices, binary codes, and network codes. Advances in Mathematics of Communications, 2011, 5 (2) : 225-232. doi: 10.3934/amc.2011.5.225 |
| [13] |
Min Ye, Alexander Barg. Polar codes for distributed hierarchical source coding. Advances in Mathematics of Communications, 2015, 9 (1) : 87-103. doi: 10.3934/amc.2015.9.87 |
| [14] |
Victor Ayala, Adriano Da Silva, Luiz A. B. San Martin. Control systems on flag manifolds and their chain control sets. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2301-2313. doi: 10.3934/dcds.2017101 |
| [15] |
Carlos Munuera, Morgan Barbier. Wet paper codes and the dual distance in steganography. Advances in Mathematics of Communications, 2012, 6 (3) : 273-285. doi: 10.3934/amc.2012.6.273 |
| [16] |
San Ling, Buket Özkaya. New bounds on the minimum distance of cyclic codes. Advances in Mathematics of Communications, 2021, 15 (1) : 1-8. doi: 10.3934/amc.2020038 |
| [17] |
Jinmei Fan, Yanhai Zhang. Optimal quinary negacyclic codes with minimum distance four. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021043 |
| [18] |
Hans-Joachim Kroll, Sayed-Ghahreman Taherian, Rita Vincenti. Optimal antiblocking systems of information sets for the binary codes related to triangular graphs. Advances in Mathematics of Communications, 2022, 16 (1) : 169-183. doi: 10.3934/amc.2020107 |
| [19] |
Luciana A. Alves, Luiz A. B. San Martin. Multiplicative ergodic theorem on flag bundles of semi-simple Lie groups. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 1247-1273. doi: 10.3934/dcds.2013.33.1247 |
| [20] |
Enhui Lim, Frédérique Oggier. On the generalised rank weights of quasi-cyclic codes. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2022010 |
2020 Impact Factor: 0.935
Tools
Metrics
Other articles
by authors
[Back to Top]